GMod 9 (PC), note that it's a FREE mod. If you weld too much stuff to too much stuff (as if you're trying to make a Katamari Ball or something), it spazzes out. ('The Blackhole Effect') It's just a big seizuring ball of death. Walk into it and you'll be punted great distances (and killed on impact). The only cure is to pull your Crossbow of Deletion and hammer some arrows into it, or take your Physgun, grabs it, and freeze it.
If you get a mass of wooden crates (or other flamable/explosive items), set one on fire, and wait a few seconds, your game will crash, and your sound buffer will loop the last two seconds.
And then there's Mingebag Behaviour 101: Go into server, spawn 50 'Huge Chimney' props, EasyWeld them to each other, and you have a lag issue (and an asshole issue).
As for other games...
Harry Potter: PoA (GameCube). I equipped my broomstick and did what anyone who could fly would do - go up. I soared upwards until Harry suddenly stopped. The camera entered the back of his head, and it looked like someone with a triggered peanut allergy, inside out.
Left 4 Dead (Xbox 360). During the Death Toll Finale, a Tank came up behind us and smacked Louis. He flew over the rooftop of the cottage and acted as if he were hanging from a ledge, despite being several feet away from it. We were oveerwhelmed because we were laughing too hard to fight.
And while I was sat on top of that roof (as a Hunter), I looked through the hole in the roof, and the WHOLE cottage vanished beneath me. It was still solid, and I could see everyone inside (hovering meters off the ground-level, no less), but I could see the dirt beneath the cottage.
In No Mercy, just after the Chopper Pilot tells you to go to the namesake hospital, you can jump off the rooftop you're on and live. Jumping into the alleyway and landing on the air conditioner can skip you the entire apartment section with only the cost of a medikit. And jumping into the main road (and hugging the wall of the building next to you can put you behind the 'Wrong Way!' fence. Walk down the road and the realistic façade peels away quick. And running into the crashed Hummer will give you a heart attack. Literally.
While this was patched recently (Valve, you assholes), you could repeatedly punch a chaingun turret and fling yourself away at 100kph (and shatter your ankles on the fall). That was an AWESOME one.
In Sonic Unleashed (Xbox 360), I fed Chip so much stuff that a single item of food more will crash the game. Now I can't get the achievement for giving him one of every food item.
Mirror's Edge, being killed in the middle of a jump or fall will make Faith slump over with her hand a'fore her face as normal, but it's unnerving to think that she's actually three feet off the ground whilst being incapacitated. You can also get down to street level from one of the rooftops in a certain level. But walking into an unknown area (unknown as in you can't see it), will violently shudder your controller and make Faith black out. If you do it right, you can go to the edge of the map and fall out. The noise that happens when you're falling kicks in and doesn't stop.
*BvvvwooOOOOOOOOOOOOOOOOOOOO...*
And let's just say the whole of Sonic 2006, which was incidentally coded by the programmers smacking their heads against the keyboard,
The miscellaneous Taunt Glitches of Team Fortress 2 (Xbox 360). The moving taunt (jump just after you hold the X button and you can move and taunt at the same time) and the switch taunt (change weapon just after you hold the X button and you will taunt with the wrong weapon). The former is cool because you can celebrate a kill without being in danger. The latter is cool because you can make crazy things happen. Heavy twirling Sasha around his finger (shotgun), the Demoman drinking his grenade launcher (Scrumpy bottle), the Engineer twirling his wrench or Construct-o-mat (pistol), the Medic playing his syringe launcher (Bone Saw). And so on...