Glitches in Lemmings

Here I will attempt to compile a list of all known glitches in Lemmings. This is for the first-generation Lemmings games: Lemmings, Oh No! More Lemmings, and Xmas/Holiday Lemmings. The primary focus is DOS Lemmings, but I will try to include ports of the original game as well.

DOS

Climbers

When a climber encounters a ceiling and falls down, it comes away from the wall by one pixel, instead of falling down right next to the wall.
Because of the way climbers check for terrain above them, they can either climb through small overhangs at the top of a wall, or fall down when there is a tiny gap (which it should be able to get into) with terrain hanging above. The outcome depends on the height of the wall.
(Original Lemmings only) Assigning the climber skill to a shrugger causes the lemming to start moving straight away, and remain in the shrugging position while it moves on.
If the terrain that the climber is on is removed, it hoists immediately and converts to a walker in mid-air for one frame, during which it is possible to assign a skill.
If a lemming trapped inside terrain is made a climber, or a climber becomes trapped in terrain, it repeatedly begins climbing, gets stuck, and falls slightly. It gains one pixel in height each time. Because climbers transitioning to fallers are shifted across slightly, the wall has to be at least 4 pixels wide for this to work.
If a lemming climbing up a thin wall encounters a blocker on the other side of the wall, it will go through the wall.

Floaters

Floating lemmings can enter exits, even if there is no terrain under the exit trigger. This only works from the moment they deploy the umbrella, not in the first few pixels of a fall.
(Glitch arguable) Floaters always survive a fall, even if they are assigned the skill near the ground and there isn't time for the umbrella to open.

Bombers

If a bomber is not placed on steel when it explodes, it removes all terrain in the explosion mask, including steel. If it is on steel, it removes no terrain at all.
Falling ohnoers can enter exits, even if there is no terrain under the exit trigger.
After exploding, the lemming's position is shifted upwards by a few pixels. (Not reproducible in the Lemmix editor, since this removes the lemming as soon as it explodes.)

Blockers

The blocker's area of influence overwrites steel and trigger areas. This makes it possible to destroy steel by placing a blocker next to it, and disable the effects of traps, one-way walls and exits.
If you assign a bomber skill to a blocker, and remove the terrain under it during the 'oh no' so that it falls before exploding, its blocking area remains in place. Any steel or trigger areas that were canceled by the blocker are put back where it explodes, instead of where it was placed.
Blockers can push lemmings through walls. This happens because lemmings cannot move towards the center of the blocking area (which is how blockers work), so a lemming inside this area can't turn around until it leaves the area - even if there is terrain in the way. (Combined with climbing in walls, this is known as the "Tame 20" glitch, after the level where it was used to achieve a no-builder solution. Note that you have to remove the blocker for this to work.)

Builders

The "Giant Leap" or "sliding" glitch: A lemming encountering a step of 3-6 pixels will "jump" up it. The game checks each frame to see whether the lemming has reached the top of the step, instead of stopping when it reaches the initial height of the step. Thus, if you can add terrain (using a builder) at the top of the step, the lemming will continue jumping.
Builders only check for terrain at one pixel above them, but they move forward two pixels at a time. This means they can build through one-pixel-wide overhangs.
Right-facing builders place bricks one pixel further in front of them than left-facing builders. This affects the potential length of a bridge that can be made by "stretching" bridges (delaying each builder assignment until the last possible frame). Additionally, this means right-facing builders can always bash when they reach a wall, whereas left-facing builders will turn around as soon as they hit the wall if they were only one pixel away after laying the previous brick.
The builder skips a check for terrain on the last brick, so if you assign a builder an exact bridge length (or slightly less) from the wall, it can build further into the wall than normal, and shrug instead of turning around.
While builders turn around when they encounter a ceiling, it is possible to assign more builders closer to the ceiling. This means lemmings can get stuck in ceilings, and build up through thin floors.
Similar to the above, lemmings can get stuck at the top of the map. At this point, it is no longer possible to (normally) assign builders.
It is possible to assign builders to lemmings stuck at the top of a map, by having a blocker under the cursor, so that the stuck lemming has second priority for selection.
Turning a builder with a blocker between placing a brick and stepping onto it causes a fake brick to appear for a moment, and leaves a tiny hole in the bridge that lemmings cannot get across.
If you assign a builder to a lemming as it turns around at a one-pixel wide wall, and then turn the builder with a blocker before the first brick is placed, the builder will go through the wall and continue building.

Bashers

Bashers check for terrain only every second stroke, starting with the first.
Bashers remove all terrain within their destruction mask, including steel.
The basher's terrain-destruction mask includes the column of pixels that the lemming is in. Since lemmings walk into the wall slightly when they turn around, it is possible to remove steel and one-way walls by assigning a basher to a lemming as it turns around.
Bashers can be stopped mid-stroke to leave a small upward ramp.
Bashers check for steel higher than they check for terrain, so they can bash through the top of steel.
Bashers near the top of the level may stop randomly. If it checks for steel off the top of the screen, the game reads from a part of memory that isn't actually written to by the game. If the value happens to correspond to steel, or one-way walls facing the wrong way, the basher will stop. (In Lemmix, the basher will always go through).
By assigning a basher where there is a wall behind it and enough terrain in front (so that it keeps going), you can place a blocker after the first stroke to make the basher flip through the wall without breaking it.
With a specific terrain formation, a basher can fall through terrain while leaving it intact. This is best observed on Tricky 5 / Taxing 8.

Miners

Miners remove all terrain within their destruction mask, including steel.
Miners can be stopped mid-stroke to leave a small upward ramp.
Apart from the initial assignment, miners only check for steel directly beneath them. This means they can break steel in front of them, and above them.
The miner's terrain-destruction mask extends one pixel behind it. As with bashers, it is possible to remove steel (though this is slightly more problematic, since there has to be no steel directly below the lemming) and one-way walls by assigning the skill to a lemming as it turns around.
Miners are positioned one pixel too low during the first few frames of their animation. This makes it possible to have the miner fall through the floor while leaving it intact for other lemmings to walk on, by assigning a blocker or bomber at the right moment.
When a miner breaks through a floor, it falls one pixel too far back, making it possible to separate the miner from other lemmings.
Miners can break left one-way walls, but not right. A miner assigned in a right one-way wall area will take one stroke and turn back.
Miners shift across by two pixels at a time, so they can cross one-pixel-wide gaps.

Diggers

Diggers will remove all terrain within their destruction mask, including steel.
Diggers check for terrain in a row of 9 pixels below them, but they only check for steel in one pixel. This means they can dig away the side of steel pieces, and even continue digging while holding on to nothing but steel.
The digger's destruction mask includes three rows of pixels: one below the lemming, one alongside and one above the lemming.
When there are two or more lemmings under the cursor when attempting to assign a digger, the game doesn't check for steel under the second-priority lemming. Thus if the first priority lemming isn't on steel, but can't dig (either because it is already a digger, or it is a blocker or 'oh-no'ing bomber) the second-priority lemming will start digging, even if it is on steel. (Note: Lemmix's replay function doesn't handle this correctly)
Digging lemmings can enter exits, even if there is no terrain under the exit trigger.
Pausing when assigning a digger skill sometimes causes a glitch sprite to appear. (Not reproducible in Lemmix)

Interactive Objects

"Direct drop": Lemmings falling onto the exit's trigger area will exit if there is terrain under it, even if they would splat from the fall if the exit wasn't there.
Lemmings falling into water may be swept across sometimes, depending on the location of terrain. With a specific setup, it is possible for a drowning lemming to be swept through terrain. (See ClamSpam02 level 5, "Get Out of the Pool!)
Object trigger areas take precedence over steel areas. This can be exploited to dig through steel.
Objects with no effect still have a trigger. In most cases, these are placed 4 pixels above top left corner, though Dirt and Crystal exit top pieces have wider triggers, placed lower down. These "triggers" have no special effect, but still cancel steel. (Note: these triggers are missing from entrance hatches in Lemmix.)

Some object triggers are misplaced:
- The water in marble tileset (green "acid") has its trigger area too high - lemmings appear to drown above the surface of the water.
- One-way walls are 4 pixels too high; in some cases it is possible to bash underneath the wall because of this.
- Brick tileset one-way walls are twice as wide as they should be.
- (Glitch arguable) Some exits have to be placed lower in order to work. For example, the Bubble tileset exit can never work unless it is lowered slightly into the terrain.

Level Stats

"Nuke glitch": When the nuke is activated, the game calculates the percentage saved based on how many lemmings have been released, not how many are available in the level.
Pausing for time: The entrance hatch begins opening a specific length of time after the level starts, at the same time the sound effect plays. If you pause the game before the hatch begins to open, the timer stops counting down while the game is paused, but the hatch still opens at the same time (or immediately after you unpause, if you wait until after the sound plays). This gives you about two seconds extra to complete the level.
(Glitch arguable) Release rate and skills cannot be selected with the mouse while the game is paused. They can still be accessed via hotkeys.
In the level preview screen, terrain off the left of the level appears on the far right of the preview picture.
Using a hex editor or Lemmix, you can set release rates above 99, up to 255, and also 0. The values simply wrap around into negatives: 255 is effectively -1, 100 is effectively -156 (one lemming per 131 frames). During play, you can change the rate to anything between this negative rate and 99 - never slower than the initial rate (Lemmix handles this incorrectly). 0 appears as a blank (the same as for zero skill counts), while values from 100 to 255 use junk characters for the tens digit. Additionally, values of 255 will blink until they are changed.

Other

"Right-click bug": If you highlight a lemming inside the cursor, then mouse over a lemming that is performing a skill, and then left-click that lemming while holding the right mouse button, the previously highlighted lemming will perform whatever skill is currently selected, even if it is outside the cursor. If the blocker skill is selected, and highlighted lemming dies in a trap before the left-click, the blocker skill will still be used, and a blocker area will be placed over the trap. (Not reproducible in Lemmix.)
Info on lemmings inside the cursor (eg. WALKER 1) remains when you quit and restart a level, until lemmings begin falling from the hatch. (Not reproducible in Lemmix)

The left side of the map acts as a wall. As with any other wall, lemmings will walk into it slightly when they turn around. With the left edge of the map, this means they are at x = -1, which is off the edge of the map. They will turn around at this "wall", even if there is no terrain under them at the moment they turn around (note: Lemmix cuts off terrain off the edge of the map, but in DOS it can continue a bit further). Some skills have unique effects when used at this position:
- A blocker assigned at the moment it turns around stops for one frame, during which it can turn other lemmings, then continues walking.
- A blocker used near the edge of the map can push lemmings off the edge of the map. If you remove this blocker, you can place another one and push the lemmings even further off the edge. These lemmings are no longer selectable, but they still exist in the level.
- If a bomber's countdown ends when it is off the edge of the level (see above), or turning around at the edge, it falls down before exploding.
- A digger assigned past the left edge of the map will dig as long as it has some terrain to hold on to, and then fall down.

Amiga

Amiga Lemmings shares most of the same glitches as DOS. However, these glitches are not present in the Amiga version:

Nuke glitch
Pausing for time
Direct drop
Continuous shrugger (assigning climber skill to a shrugging builder)

Sega Master System

Miners can cross one-pixel gaps.
Climbers come out slightly from a wall when they hit a ceiling and fall.
Diggers float in mid-air for a brief moment during their animation. If you assign a blocker at this moment, the lemming will fall and become a walker.
The clock blinks when there are less than 30 seconds remaining. If you pause while the clock is visible, and unpause when it is invisible, the timer won't count down. Thus you effectively have unlimited time for every level.
Pausing the game when a shrugging lemming reverts to a walker causes the lemming to glitch out and cycle through animations. The lemming doesn't move in this time, making this an effective method of slowing down a lemming.
(UNCONFIRMED) Repeatedly pausing and unpausing can cause bashers to stop moving, while walkers continue on.
Bashers can pass through blockers, if timed well.
When a digger finishes, it becomes a walker for a moment before falling. At this point, it can be assigned to bash or build in mid-air.
Lemmings falling into water become walkers for a moment before drowning or dying to a trap (unless they have fallen too far, in which case they will splat). It is possible to assign a builder in this time, and build a bridge from the water trap. On fire objects, a second lemming is needed - the first burns after placing one brick.
On levels with multiple entrances, when you build over one entrance, the bricks are copied onto other entrances. The same applies to exits, on levels with more than one of those. The copied bricks are solid terrain, not just graphics.
Falling lemmings appear to repeatedly change the direction they are facing.
Building on continuous traps (see above) disables them. Their animation freezes, and they behave as solid terrain.
Bridges overlapping entrances/exits (including copied ones, see above) are indestructible, like steel.
When the nuke is active, lemmings sometimes drown (when they would otherwise splat - see above) when they fall into water from above the splat height.
Using a miner on steel causes the lemming to move backwards a little (note: they do not turn around in this version). With enough miners, you can effectively walk backwards.
If a bomber's timer runs out at the same time as the lemming would splat, it falls into the terrain slightly before exploding.
Through repeated pausing and unpausing, it is possible to make a basher "slide" through a wall without destroying the terrain. This even woks with one-way walls with arrows pointing the wrong way.
A digger starting on a peak in the terrain will just take out the top of the peak and then walk on.
Walking lemmings appear to bob up and down at random when there are many lemmings on the screen.

Windows

The maximum safe-fall distance is incorrectly set to 66 instead of 63. This makes some levels much easier (eg. 'We all fall down').
Lemmings can walk over the top of the level.

PSP

Lemmings can walk over the top of the level.

Mac

Some terrain objects are slightly taller due to the high-resolution graphics. This can cause lemmings to turn around in places where they wouldn't in other versions. Mayhem 26 is a famous example.
Digging skills and bombers remove all terrain within their destruction mask, including steel.
Climbers climbing up to the top of the level can become trapped in the terrain, instead of falling back down.
In some cases it is possible to bash through one-way walls in the wrong direction. This is likely due to misplaced trigger areas, as in DOS.