Following on from the recent discussion in the Level Review Topic, I thought I'd ask -- what levels did you take a long time to pass the first time you encountered them? This will include both easy-in-hindsight levels that were tough for you at the time, and difficult puzzle levels that took you a long time to find the solutions.
Since I expect most of you will have more stories to tell about the version you played first, it would be helpful if you stated which that was. For me, the black-and-white Mac version, although we finally bought a colour machine a few years later.
Anyway, here's my list of levels that had me stumped for a while -- with the asterisk marking ones that were real roadblocks, i.e. at least a year:
Fun 24 -- I found this RR 99 level difficult to handle at the time
Tricky 14 -- took me a while to get used to playing with music off, as I could not stand the music for this level!
Tricky 19 -- a challenging puzzle for its position in the game, especially for me as I never thought of the solution with the miner
*Taxing 11 -- I honestly never thought of using a dig pit, and was trying to do this with miners and builders!
Taxing 28 -- I never thought of the solution with the climber....
Mayhem 2 -- very daunting and looked impossible to begin with (and then I beat 3-9 in the same night!)
Mayhem 14 -- impossible on the b&w version, had to wait until we upgraded
Mayhem 21 -- the one level I couldn't solve and had to get a friend to help me with
*Mayhem 26 -- Mac version. 'Nuff said.
Crazy 8 -- I found it difficult to manage the precision and crowd control on this level
*Crazy 10 -- a gorgeous puzzle but way too hard for its position
*Wicked 3 -- another beautiful but very difficult puzzle, still perhaps my favourite ONML level
Wicked 6 -- yay, bomber timing!
Wicked 18 -- horrendous level by anyone's standards; didn't help that I was terrified of the icicle traps so I wouldn't even contemplate attempting a "low road" solution
Havoc 7 -- multi-tasking heaven
*Havoc 16 -- an absolutely fiendish puzzle to introduce the "Big Five"; I think all of them except 18 probably took me a while, but this one certainly the longest
So, what were yours?
The worst ones for me were Tricky 19, Taxing 11, Mayhem 23, and most of all, Mayhem 29.
The first three took me a good couple of weeks each before I finally passed them, while Mayhem 29... well, I completed the entire game sans that at age 5 (using a code to get to Mayhem 30). It wasn't until 6 years later I finally managed to beat Mayhem 29. (and I tried MANY times throughout those 6 years)
For me, I was stumped for a while on Fun 13 and Tricky 2, then Tricky 7. I had no problems with Fun 24 or Tricky 19. Tricky 10 was fairly hard which took me a few days to solve, and then how about Tricky 23. That was hard as well.
This is possibly a derivative of the "Most out of place levels" topic by namida. Don't you realise that?
Original Lemmings:
I never had problems with the Fun set. I think the absolute very first time I picked up Lemmings when I was like 9 I got to Fun 11 and couldn't crack the OWW, but I don't remember any other fun levels being that hard.
Tricky 19 was the first really hard level in the game, I mean it's a great puzzle but I had a very hard time conceptualizing it. After that
Taxing is hilarious because all the hard levels are in the first half of the set:
1: Yea, I as a kid could not see how to get through 3 pillars with 2 bashers. The route I finally DID find was the below-route, which took me a while to execute because of the timer.
3: I used miners to crowd control, not diggers for some reason. The result is that all the lemmings were spread out and I always kept running out of time. It didn't help that I count hold the lemmings back very often so as a result I hated this level and gave up on it for a while.
11: Didn't give me quite as many problems as 3 but I still remember it for how freaking hard the first step is.
13: The first major (several month) stumbling area for me. Basically every solution I found either lacked a skill, or trigged one of the stupid terrain glitches. I still remember the one time I actually had and executed a solution with exactly the skills given, went to place the last miner, and OOPS GAME GLITCHED MINER TAKES ONE SWING AND TURNS FOR NO REASON AH AHHAHAAHAHAHAH. I hate this level so much.
After that I plowed through most of Taxing in a day, I think Triple Trouble was the only remotely hard level for me after that.
Mayhem:
5: Wow, this level. It took me so many tries to get the building up to the exit to work. This one stopped me for months too, as did
9: Execution levels with no major puzzle to them were really hard for me, because I saw how to do it and then never could get it to work. This and Taxing 13 was where I was stuck when I quit Lemmings for a couple years.
20: After finally getting 9 everything after was simple until this one. This is a really good puzzle which gave me tons of problems. I didn't give up on it but it still took me a solid week straight of messing around with until I found the solution.
29: Again, execution level. Didn't give me a TON of problems because hey I'm only 2 levels from the end finally but it still took me a while.
ONML is a bit longer so yea I'll post that later
13: The first major (several month) stumbling area for me. Basically every solution I found either lacked a skill, or trigged one of the stupid terrain glitches. I still remember the one time I actually had and executed a solution with exactly the skills given, went to place the last miner, and OOPS GAME GLITCHED MINER TAKES ONE SWING AND TURNS FOR NO REASON AH AHHAHAAHAHAHAH. I hate this level so much.
Good to know I'm not alone here. Although I think when this happened to me, it wasn't actually the first time I played the level. It's possible that the first time I solved it might have been on the Windows version, where the one-way glitch doesn't happen.
Other tough ones for me were:
Tricky 16: Multiple bomber timing... bad enough to sneak into my "bottom 5".
Tricky 19 (once again, it seems I'm not alone here): The idea of digging and building to turn around was foreign to me at this point.
Tricky 30: I guess this doesn't really "block" anything, but this map with no bashers is tough. And the time limit is quite harsh too.
Taxing 1: Same reasons as mentioned above (and my first solution was the floor route too, IIRC)
Taxing 13: oh right, I mentioned this one already.

Mayhem 1: A real "barrier to entry" to the last set of levels. Making your builders go the distance is difficult the first time around...
Mayhem 5: Having to contend with some suspect game mechanics... not nice.
Crazy 2: Hey, I just did a review of this level. Too hard for level 2.
Crazy 16: Containing and releasing the lemmings with only 3 builders available is far from simple.
Wicked 1: Some times when I played this level (unlocked from the start, of course), I remembered the solution... and other times I didn't.
Wicked 10: For some reason, I kept running out of builders here... can't remember why.
Havoc 5: We all know how tough this one is...
This is possibly a derivative of the "Most out of place levels" topic by namida. Don't you realise that?
Not at all. There may be a slight overlap, but I would hardly call it a derivative, for two reasons. Many if not most of the levels mentioned in namida's topic were those that were too
easy for their positions, and so don't belong here. And many of the ones mentioned here are very hard levels, but not too hard for their positions (e.g. Taxing 28, Mayhem 29, Havoc 16) and so don't belong in the other topic.
In response to other people's posts:
I agree with Insane Steve's list of difficult Taxing levels, and might have mentioned all of the same ones myself, were my list not long enough as it is. (I should have included Taxing 6 on my list, though; that was an oversight.) I did actually find the real solution to Taxing 1, and the miner glitch on Taxing 13 isn't in the Mac version.
No, I don't know how tough Havoc 5 is.... it's a neat demonstration of a couple of nice tricks, but I've never thought of it as being a particularly hard level....
All of my Lemmings roadblocks came from the Master System version. There were many levels I had to work on, but the ones that stand out are:
Tricky 19 was my first major roadblock. I was trying to rescue all the lemmings until I realised I could sacrifice one. I cleared the level on my next attempt by utilising the blocker.
Tricky 22 threw me off completely. I eventually solved the level by using builders, but I did not rescue 100% at the time.
Tricky 30 held me for a while because of the time limit.
Taxing 01 was eventually solved by bashing underneath the pillars. It was my dad who came up with the idea.
Taxing 03 stalled me, once again because of the time limit.
Taxing 11 took me ages to sort out. Either i'd leak the lemmings out of my dig pit, or when it came to crunch time, the builder built the wrong way! >.<
Taxing 23 was a hard lesson on the conservation of builders.
Taxing 26 is too hectic. That had me stumped for a long time.
Mayhem 01. I wasn't doing this level properly, and I kept banging the head of my builder.
Mayhem 03 was tough to work out. You know how it is.
Mayhem 19 is more difficult on the Master System because the walls are thicker (especially the second wall). They're kind enough to give you two blockers, but so much can still go wrong.. and for me, it did. Too many times.
Mayhem 26 is also tougher on the Master System, though not as much as level 19. The big problem is most of the walls are too thick for bombing.
Playing the DOS version for the first time, I had to get used to the different physics, and some levels required different strategies (especially Mayhem 20), but other than that, I didn't get too stuck on any of them.
I remember I had a lot of problems with "There's madness in the method". As for original Lemmings I don't recall since I was 8 when I played it
I never had many problems with Havoc 5, actually. The trick I caught on to rather quickly.
Havoc 4, though...
No, I don't know how tough Havoc 5 is....
What? Haven't you played this level yourself?
One advantage to keeping a book of access codes is that it makes it easier to look back at things like this

In my book, the level names and codes for Havoc 1-7 are all written with the same pen, so they can't have taken me long (although I do remember finding 4 quite tough).
I think I never really had a linear road through the levels, as ages back in elementary school I rarely played computer (and if I did, it was almost exclusively Supaplex), and when I rediscovered lemmings, it was on WinLemm, which allowed you to skip back and forth between the levels.
I think I skipped a lot of levels, and concentrated on ONML Havoc. And somehow
Havoc 5 (There's Madness in the Method) stood out to me (glad to know I'm not the only one).
While there were also other levels I hadn't solved at that point, this one somehow got me to want to solve it at all costs, possibly due to it's simplicity; and I remember the MIDI of 'Rondo alla Turca' playing in the background all the time. After a few days I eventually got it.
There were more unsolved levels left (I think Havoc 4, 7, 8 and some of the later ones I don't remember; perhaps the stats are still on my computer back home), but at this point I got into editing and playing custom levels (Primarily Insane Steve's Cheapo sets). As I made a list for the level I solved, I guess I could find out these roadblocks, but that's not the point of this thread... It was Isu's Cheapo version of Genesis Mayhem 30 "Lemmings' Ark" that I played first, and which took me a week to solve.
When I came back to the original levels with that experience from the custom levels, only very few of them were of interest anymore, though these leftover Havoc level I mentioned earlier were still not that easy:
Havoc 4 (The race against cliches): The time limit and the pillar heights make the obvious approaches very difficult or impossible.
Havoc 7 (Creature discomforts): I somehow had problems with the skill management there, always being short of something. I also realize that I tool the wrong builder route on the right side.
Havoc 8 (Lemming about Town): Somehow always one builder short if I remember correctly.
Don't remember about the later ones, Havoc 15 and 16 might have been amongst them.
Another one is Wicked 1 (Lemming Tomato Ketchup Facility): I didn't immediately find a decent approach to it.
When I played the Genesis version later, there were still a few levels that took me a while (i.e. more than one hour) to solve:
Present 27 (Try anything once): I just remember having trouble with this one, I likely overlooked something there.
Present 28 (Which one are you trying to get?): Having to close the lava pits with the limited vertical terrain removing skills and only one climber gave me some trouble.
Sunsoft 21 (Be sure to be a builder): Was pretty difficult for me to get at least one lemming up with all the obstacles making building difficult.
Sunsoft 24 (Out, away from the tune): I somehow overlooked the clean standard route (i.e. bashing through the third note) to it, and tried to come up with something different and messy.
Present 27 (Try anything once): I just remember having trouble with this one, I likely overlooked something there.
You did, because that level has two of the hugest backroutes (or maybe you want to count it as one backroute with two different implementations) of any Lemmings level in existence

Although I found the real solution first and didn't find it too difficult.
None of the Genesis levels had me stuck for very long, but I remember the ones I had most trouble with were "Just a Minute", "Evacuating a coal mine" and "Let's go camping" (which I eventually solved by the backroute -- for this and "Final impediment" I never found the real solution).
Ah yeah, either I found that backroute only later, or I set myself to solve it the regular way back then (considering the obviousness of that 4-skill backroute, it seems difficult to overlook).
Just re-played "Evacuating a coal mine", and it's indeed not that simple. I don't remember it for giving me trouble though.
I don't really know what's intended for "Let's go camping", how many lemmings are you supposed to send down for the intended solution? All three?
For "Final Impediment", you're referring to a short-cut that doesn't go along the bottom (I don't remember my solution to it that well, but I think it went the long way)?
All three, I'm fairly sure. I know ccexplore found the intended solution but I asked him not to tell me the details so I could continue looking. And "Final Impediment", yes, is possible to do with just five builders without any lemming going to the bottom.
Ok, I found a solution for "Let's go camping" sending three lemmings down.
It's pretty clean, so I suppose it is the intended one. Very elegant, actually.
Before finding this one, my previous strategy was only one or two pixels short of height for the final bridge, as timing forced me to start building near the bottom of the tent. This solution however would have employed the block hanging in the air near the tent, which I see no use to.
EDIT: Ah, ccexplore is back! Though I suppose our solutions are identical, if we both dare labeling them 'intended' solution.
Obviously there's also solutions sending down none and one, and I sort of found also a solution sending down two, though it's pretty cheap, delaying the second lemming at the top till all work is done, and then having him come down just for the sake of it. My attempt at a proper solution had the same problem as my first attempt at sending down three: a few pixels too low at the end.
My roadblocks are from PC DOS version, and they are mostly same than the aforementioned levels.
Lemmings:
Tricky 19: Postcard from Lemmingland - I can't remember playing this level, but levelcodes in my old levelcode paper stops in this level in Tricky rating, so it had to be some kind of a roadblock for me too.
Tricky 23: From The Boundary Line - This one was freaking hard! I passed Taxing all the way to level 26 and Mayhem at least to 13 before beating this. I had problems with RR 99 and the pit, from where you can't get up with that single builder. When I last played L1 marathon, this was the first level in the whole game I had to restart and I'm quite sure I had to give it at least third try to pass it.
Taxing 13: Upsidedown World - I remember this one being really demanding but I can't recall how long it took to solve this.
Taxing 26: Triple Trouble - I can't remember "Call in the bomb squad" and "POOR WEE CREATURES!" from my childhood, and this memorable level is the reason for that. Assigning skills to lemmings facing the correct direction caused troubles for me, and I think that I always wasted too many builders.
Mayhem 13: The Great Lemming caper - I can't remember this level either from my childhood, levelcode paper stopped in this level. But I remember that I was very satisfied when I beated this for my first time about 9 years ago!
Oh No! More Lemmings:
Crazy 10: ROCKY VI - Yes, solving this took long... Maybe even longer than solving all the Wild-levels! (I'm not 100% sure about that, I derived it from the old levelcode paper.

)
Crazy 16: Across the Gap - Insanely hard level when I was a kid. 100% requirement and few builders caused troubles. This level is like a counterpart of Tricky 23 for me being such a tough level in the second-lowest rating in the game.
Wild 3: Lemmings Rhythms - This is the hardest level in Wild rating for me.
Wicked 2: Inroducing Superlemming and
Wicked 3: This Corrosion - These both levels were very tough barriers for me preventing access to the later Wicked levels. In Wicked 2, I always got my lemming knocking his head to the ceiling and turning to his death at the end of the level before finding the solution. I always solved Wicked 3 using the left path, and I was really amazed when I found the right path solution in autumn 2010!
Havoc 5: There's madness in the method - The greatest roadblock of all time for me in Lemmings games. Never thought that you needed to multitask with those basher and miner lemmings at the left part of the level. One day I gave up and searched the levelcodes from the Internet for the rest of the Havoc. I also found Havoc 15-20 extremely difficult.
I've played other Lemmings games for my first time so recently that no one level became a real roadblock for me, even though there are many levels that would have easily been such a thing for me if I would have played them when I was a kid.
I had DOS when I was a kid.
now use miners and climbers - when I first played I think I didn't look at the skills and see the miner right away so I was stumped on this for a little while
worra lorra lemmings - It was just generally 'taxing' for me and I usually ended up messing up right near the end so I had to start over so many times I eventually gave up and stopped playing.
Lemming Drops - same as above
Postcard from Lemmingland - This is the roadblock which prevented my solving the game until I was a teenager.
From the Boundary Line - I just couldn't think of the possibility that you need to lose a lot of the lemmings in the beginning.
The Prison - another just taxing level I never really liked much
Steel Works - I had no problem with the first part (taking care of the high up entrance) the building was difficult. i always ran out of builders
the great lemming caper - a tough puzzle level for me, though I liked this one a lot.
no added colors or lemmings - same as above
A lot from ONML. Notably; Lemming Express, And now the end is near (for reasons I mentioned in another thread; Windows version makes it hard), Lemming Rhythms, It's a tight fit. Lemming Tomoato Kechup Facility, Pop your top(s).
Lemmings Revolution;
How do we get up there?Can't get there from here - I actually solved this level before solving 'Time to get up!' in OL, so after wooping this level I went back and solved that. (discovering the climb/bomb trick)
Bridges - the thing with acid lemmings walking on an empty pool is just weird and not at all logical imo so I had trouble figuring this out.
Just you wait, My Finest Moment, Nice Shootin' Tex, Hit n Run, Don't Let Them Out!...
Maybe I'll complete my roadblock list a little more because I realized that there are official levels that I haven't even passed yet! These games I've played for my first time this year except Lemmings Revolution which I played as kid as well as L1 and ONML, so these aren't super roadblocks (like in my L1 and ONML list), and they didn't stump me more than two days (except Lemmings Revolution levels).
Xmas & Holiday Lemmings (DOS):
Hail 5: Get the Point? The only christmas level which stumped me really. I had to think this over a night and I ended up with a solution in which I builded from the ice peak and turned the builder with a blocker and then released the blocker with digger or something..
Genesis/Megadrive levels (played in Lemmix):
Taxing 2: Temporary peace - The first Genesis level I had to try many many times. I used brute-forceish pixel perfect execution strategy and didn't notice the wood sticks above the entrance..
Sunsoft 24: Out, away from the tune - Like geoo, at first I overlooked bashing the third note.
Lemmings 2 (DOS):
After getting used to the gameplay I golded all the levels in about 4 days except...
Sports 10: Take up Archery - What the...?! My best solution for this gives me silver. I still haven't golded this, I always get frustrated with this most annoying Lemmings level ever.

Lol I have to nail this level someday myself!
Other Lemmings 2 levels which I had to think longer were
Highland 4: A mere stone's throw and
Sports 7: The Sun Sign Selection. They were strange for me, too.
Lemmings 3 (DOS):
Classic 4 - This was a tough puzzle for me when I was just getting used to the gameplay.
Classic 24 - Executing the solution and time limit caused me some difficulties.
Egypt 22 - I don't know why this took also a while to solve.
Shadow 18 - The grenade level.

For me the biggest roadblock in L3 since I played both Classic and Egypt tribes through before passing this.
Lemmings Revolution:
12-5: No clues... hee hee hee! - I beated this level using reset a bomber glitch for getting access to the laser gate. I thought that the level had some kind of a mistake like "'Tanks' a Lot" in the older patch.
12-14: It's Going to Take Time - A massive level with lots of multitasking.
I still haven't beated two Revolution levels, they are:
12-9: Turn on! Tune in! Switch on! and
12-11: My finest moment - Seriously, I have to try those again some time.
Lemmings Revolution:
12-5: No clues... hee hee hee! - I beated this level using reset a bomber glitch for getting access to the laser gate. I thought that the level had some kind of a mistake like "'Tanks' a Lot" in the older patch.
12-14: It's Going to Take Time - A massive level with lots of multitasking.
I still haven't beated two Revolution levels, they are: 12-9: Turn on! Tune in! Switch on! and 12-11: My finest moment - Seriously, I have to try those again some time. 
Me and GuyPerfect found 100%+glitch free solution to No Clues
(in case you didn't know and wanted to do this yourself; you guide the weasels to flip the laser gate!)
It's pretty ingenious I think, but I think the intended solution to No Clues is to just let the lemming that trips the laser gate die.
I have one level that I haven't beaten yet in Revolution. "Don't Let Them Out". Everything I read says that you need to bash under the one-way-wall. This always seems like a backroute to me and I've always thought they forgot one basher. With one other basher it would be possible (I think) to go around and do what seems like the correct way. The only way I've seen it solved utilizes the 'build through a thin floor glitch'.
[I lied, I have beat that level before (years ago in another 'playing']
Those last two are both good (and very hard) levels.
My finest moment has the "'Tanks' a Lot" mistake but it can still be solved a few different ways.
the other one has a really neat solution but I don't remember exactly how I solved it. I always forget on that one and it's not on the fun part. Getting to the fun part is difficult.