I have a whole truckload of glitches!
1. Pull rings disappearing, making it impossible to finish the game (Pull rings are those rings that Abe can pull to open trapdoors and the like)
Solution: Level select cheat
2. Falling down a hole while riding Elum, but Abe's head remains on the screen
3. Abe disappearing glitch (there is an entire thread on it started by Guekko)
4. Scrabs respawn after falling down a hole
5. Killing native Mudokons adds to your casualities in your Quarma (Is that supposed to happen?)
6. Too many things happening on screen causes the game to freeze
7. Aslik's executive office is gased and Abe manages to remain alive by reading the directory next to the well (random much?)
8. Collecting more grenades when you already have some (when I did this, the number of grenades I had was replaced with a smaller version of the yellow Mudokon face that appears in secret areas

)
9. Abe stops regenerating after he dies (that might have happened in the demo)
10. Blue Soul Ring (Shrykull power) runs out and the ring disappears
11. A Red Soul Ring (explosion power) comes out of a landmine and blows up everything on the screen

(also from the demo)
12. Sligs, Flying Sligs and Glukkons glow when possessed.
How to do it: Possess a Slig, Flying Slig or Glukkon. As soon as Abe's possession powers touch that creature (and make it glow), pause and Save. Quit the game and load your save file. When it loads, take whichever creature you possessed and leave the screen. Your possessed creature should now be glowing.
NOTE: This glitch does not always work so don't be disappointed if nothing happens.
13. Abe is suffocated by gas while in possession of a Slig, but you can still control the Slig
14. Abe can climb down THROUGH a solid floor
15. If you use a Yellow Soul Ring (healing power) in a screen with Tear-X-Tractors, a Mudokon will stand up in the Tear-X-Tractor and be cured of his SoulStorm sickness
16. Bird portals disappear in certain areas (such as the beginning of Stockyard Escape) and Mudokons are forced to be left behind
17. Elum stops respawning after you die (I'm not sure if that is actually a glitch)
18. Rocks and meat can be electrocuted if throw through electric walls
19. Native Mudokons miss when aiming at you with their slingshots (I'm not sure if that is a glitch either)
20. Bees avoid Native Mudokons and always go after you
I'll try to get screenshots showing some of these.
Quick bit of trivia:
Did you know that Elum is bullet-proof?
EDIT: I have screenshots!
One is of A slig shooting our bullet-proof friend Elum. Another (it's hard to see) is of a rock getting electrocuted. The rest are of the glowing glitch, including the glowing fart!