I've experianced a few glitches with both AO and AE, but mainly clipping glitches where Abe or other things accidently go through walls or fall through the floor.
In Abe's Exodduss I always loved to make sligs, scrabs and farts, etc glow green, by quicksaving as I was possesing them. :P But that's already been mentioned here. Something that hasn't been mentioned here though:
In AE (again), go to Bonewerkz. In Annex 7, you can get the Shrykul and also can walk into some electrical barriers. :P What do you get if you walk into an Electrical Barrier while being a Shrykul?
Well, firstly, you glow. Secondly, you become invincible, similar to the invincibility cheat on the PSX version, but it's very, very glitchy. If you fall down even a tiny way, unless you do a standing jump, you die. If you do a standing jump off a ledge, you jump and fly for miles. :P If you get blown up by a bomb, you turn invisible, but you're still alive. If you chant while invisible, you become visible again, except you're black.
Because you die simply by falling a short way (there's a part further on where you have to climb down a ledge and drop a small way), you can't get very far with this glitch. Oh yeah, and you lose access to the menu because the game thinks you're dead, even though you're not.
Fun glitch though. :P Load up AE and try it.