Starting a new post for new results:
Space X: improved to 8 skills. A slight modification of my 9-skill solution that finally can get everyone out of the pit in 2 skills instead of 3. See spoiler/screenshot for details.
Beach V: improved to 3 skills by eliminating waste of skills purely for crowd control. See spoiler/screenshot for details.
Beach VII: improved to 10 skills. The standard solution actually is doable in 11 skills if you do it right. For 10 skills, we take a shortcut using some precision moves with the tree left of the red bucket. See spoiler/screenshot for details.
Beach X: improved to 4 skills by eliminating waste of skills purely for crowd control, using some precision moves. See spoiler/screenshot for details.
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edit: added more results below Mar 21 2010]
Circus V: standard solution improved to 4 skills, again by minimizing crowd-control skill waste. See spoiler/screenshot for details.
Egyptian IX: got 8 skills via a crawling route. See spoiler/screenshots.
Egyptian X: improved to 7 skills, thanks to one of the glitches ClamSpammer discovered a while ago, making it possible to get a lemming outside the pyramid in 3 skills. See spoiler/screenshots.
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edit: start new zip file for new results below]
Polar II:
improved to 5, no 4 skills. Most likely a slight improvement to the same solution LemSteven first reported. (Actually on second thought, maybe this is totally new.) Borderline glitch(es)? See screenshots/spoiler. Okay, I've now improved it down to 3 skills
! See spoiler/screenshots for details.
Polar V: improved to 8 skills. Miscellaneous improvements from standard solution. See screenshots/spoiler.
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edit: more results, I think Classic is the only tribe left that I haven't looked at in detail]
Polar III: finally improved to 3 skills. Took forever to come up with where to rope to trigger crawling. See screenshots.
Polar IX: improved to 6 skills. Another roper-induced crawling, a little easier to discover. See screenshots/spoilers.
Shadow VIII: improved to 5 skills. And you don't even need the cannon-pause trick! See screenshots/spoilers.
Shadow X: improved to 8 skills. See screenshots/spoilers.
By the way, Simon, there's a typo in your table. Space X is 8 not 6. The total for Space (54) is correct though.
Space X: have 1st lemming out bazooka to the left at the position shown in screenshot A. This will fling the 2nd lemming (our hero) barely out of the pit, as shown in screenshot B. When hero walks to about the center of the middle of the 3 steel blocks, have the lemming in the pit that just turned around the left wall to fire bazooka to the right (screenshot C). Then quickly assign hero runner and then jumper at exactly the positions shown in screenshots D and E. The running jump plus the bazooka explosion's knockback, timed correctly, will be able to get the hero onto the exit platform (screenshot F).
Hero will fire bazooka to turn himself around, then pour glue. Let him run back to the left and into the right half of the pit. Now wait for everyone to come out of the entrance, then have hero fire bazooka to the left, pressing against the barrier separating the two halves of the pit (see screenshots G). This will accomplish 3 things:
1) fling your hero out of the pit so he can exit
2) completely remove the barrier (for some reason, it wouldn't work quite right if you try to do this from the left half of the pit)
3) the knockback will fling the crowd against the left wall of the pit, resulting in the crowd being more compressed
The compression of the crowd will enable you to get everyone out using just one more bazooka (screenshots H and I).
Beach V: Starting fencing through the obstacle at exactly the position shown in screenshot A. This will work out to create maximum (well, sufficient anyway) separation between frontmost lemming and the one behind it, when fencer breaks through (screenshot B). Then have the front lemming build, and as soon as the build brick is laid down, even before he steps up onto it, start pouring (screenshot C). The glue will be ready just in the nick of time to ensure everyone gets to the exit (screenshot D).
Beach VII: Here's the shortcut: when the hero lemming gets to near the top of the tree left of the red bucket, assign him miner at exactly the position shown in screenshot A. Now watch the miner's animation and wait until he starts taking a step down, then assign him jumper (screenshot B). His jumping will reflect off the tree's leaves on the right, make him end up on top of one of the tree's left leaves facing left (screenshot C).
Beach X: Scoop at exactly the positions shown in screenshots A and B, as soon as possible. The end result will be screenshot C, in which you maximize the separation of the frontmost lemming from the rest. Then complete the rest of the path using 2 archers, as shown in screenshots D-F.
Circus V: The only crowd control is to have 2nd lemming bash at position shown in screenshot A, to give sufficient delay to allow first lemming to platform to seal off the right end. Then have lemming scoop to the left near the top, at position shown in screenshot C. This will basically allow him to break through so close to the top that it only takes one platform-brick to bridge the gap to the exit, which you can do in time (screenshots D, E).
Egyptian IX: Bash through the first obstacle, and then start stomping very close to the trap trigger (screenshot A), which should prevent anyone from triggering the trap. Then use a basher, 2 stompers and 2 bombers to pave the way through to the area below the exit (screenshots B and C). Note that you must assign the final bomber at a height below the nearby steel block's top surface in order to break through (screenshot B). This is possible because the stomper stops stomping only after he gets below the steel, and if he's sufficiently to the left, the leftmost columns of pixels of the stomper tunnel will be off the steel and therefore can be taken out. Finally platform at place shown in screenshot D to trigger crawling.
Egyptian X: ClamSpammer's hopper glitch--if you assign someone hopper just as he turns around from a wall, he will start hopping vertically up the wall and through any ceilings that may be present.
To use it here, have the first lemming shimmy near position shown in screenshot A. He'll shimmy on the ceiling corner for a pixel or so and then turn around heading left. Now apply hopper glitch to that lemming as he turns around at the left wall.
Just before he completely goes through, at position shown in screenshot C, assign him sand pourer. This is to stop his hopping there, which allows him to continue going to the right--if you just let it naturally hop out, he will end up heading left instead.
Now get to the area below where the crowd is trapped and free them with the mortar. It should be obvious how to do so with 1 slider, 2 glue pourers, and 1 mortar.
Polar 2: The two key ideas:
1) you can break through the floor using two well-placed flamethrowers.
2) you don't need the skater! Due to a quirk with the way the ice works, each time a slipping lemming went back and forth once, he will actually drift slightly (maybe a pixel or so) in the direction he was facing before he began slipping. So gradually he'll move off the ice if given enough time.
This leads directly to the 3-skill solution: fence through the snowman, then after the lemmings turn around at the tree heading left, assign flamethrower at the positions shown in screenshots A and B (basically as far bottom and then to the right of the valley, and then same of the pit from the first flamethrower).
This will break through the floor, creating a path where all lemmings fall onto the ice facing left. Now fast forward and wait. The slipping lemmings will gradually drift left and will eventually exit. The first one to exit is when the clock's around 1:40, and the last one around 0:14 (screenshot C). The reason there's no 2-skill solution is because if the lemmings fall onto ice facing right, you'll run out of time long before many of them can exit.
Polar 5: 1st lemming out rope to the tree on the left immediately, as quickly as possible. The 2nd lemming out will overtake him, but the idea is to have the 1st lemming out be following as close as possible to the 2nd lemming out. Now, when the 2nd lemming out (now at the front) is close to the snowball left of the tree (screenshot A), assign him bomber. The 1st lemming out (if you did the roping quickly so that he stays close) will overtake the 2nd lemming just as the explosion occur, causing him to the flung to the left, hit his head on the treeless island above, and turn faller (screenshot B). The flinging and the lack of swooning will put him far ahead of the crowd (screenshot C). Now just finish the rest of the path to the exit (screenshot D). I've failed to find a way to do so in less than 6 skills.
Polar 3: the screenshots tell you exactly where and how to rope to trigger crawling to the exit area.
Polar 9: screenshot A shows you a spot you can build to seal off the left end of the starting platform without losing anyone. Then jump a lemming up on the left to prepare the rest of the path to the exit. Screenshots C-E show where to place the cannon, and where/how to rope to trigger crawling. You'll also need to use the cannon pause trick (see geoo's reply #13) to ensure not runing out of time.
Shadow 8: bash to the left at the bottom of the slope (screenshot A). After the basher breaks through, a lemming will overtake him. Just as that lemming starts to fall (screenshot B), assign the basher bazooka. The timing of the knockback from the bazooka will knock the falling lemming into one of the pixel-sized protrusions off the column below and to the right (screenshot C), allowing him to platform from there to create a step to make the fall safe for everyone (screenshot D). (The knockback also turns around nearby lemmings in the bash tunnel to ensure you have enough time to platform.) The rest is obvious.
Shadow 10: Assign 2nd lemming out SuperLem as soon as possible, and immediately pause. Switch skill selector to builder, and when the 1st lemming out has past the middle of the smaller steel block, assign him builder (screenshot A) and pause immediately. Move the mouse cursor all the way to the right past the 3 traps, to the upper-right corner of the steel block before the fall (screenshot B). Unpause and wait for SuperLem to fly to the cursor and crash there (screenshot C), pausing immediately when the crash occurs. Make the builder pour glue now, and then when a walker lemming is up on the glue platform and past the leftmost trap (screenshot D), make him pour glue too. The resulting glue platform will span past all 3 traps.
Back to your former-SuperLem (aka hero), have him build at the very edge before the drop to water, and then as soon as the build brick is laid, have him pour glue. As shown in screenshot E, most of the glue will span across the water-gap, and then there'll be just a little bit left over that will end up at the bottom of the right edge, creating a step to make the fall safe.
Make hero plant at exactly the position shown in screenshot E. The plant will span the gap in question, and will also cause your hero to turn left immediately after planting, giving sufficient separation for him to build over the pit before the exit in time for the crowd (screenshot F).