Those are some great videos, especially the Skate one. My personal favourites always come from the GTA series. One of my favourites is from San Andreas, where there was a hidden interiors overworld where you could use a jetpack to fly through the sky and discover all the interiors in the game floating up there, even ones that weren't used.
http://www.youtube.com/watch?v=Yfr8CnBfTNU

A recent bizarre glitch for me happened at the end of a speed run through Shadow Complex. Jason was wearing the fusion helmet when I finished but this ending cut scene has him sporting a white and purple paper-mache fauxhawk and purple guyliner. Crazy!

http://www.youtube.com/watch?v=466P1P7gDJ4

I had the misfortune of experiencing the twin Altair glitch in Assassin's Creed. That entire sequence of the game was a technical disaster.

I recently played Ico for the first time (vague Ico spoilers ahead) and experienced a massive glitch with the scene and "battle" with the Queen at the end. First, when I reached the Queen's lair, the cut-scene wasn't triggering, and randomly triggered while I was in a corner of the room trying figure out what to do. As such, I was stuck in this corner with my face to the wall during the cut-scene while I was apparently having this conversation with the Queen.

I use the term "conversation" loosely, as the dialogue kept repeating itself. Both the Queen and Ico kept repeating the same line over and over, but the sub-titles weren't showing, so I wasn't actually sure if the repetition of these lines made sense in the conversation, to which I later found out online that it didn't.

Then out of nowhere, it cut to the "battle" with the Queen, which is supposed to be nothing more than you blocking her spells with your energy sword (which the sword automatically does for you) as you rush up to stab and kill her... Yeah, I wasn't so lucky. The sword decided not to block her attacks, killed me, and my screen went black and froze.

Seeing as there isn't a save point between when you open the massive gate in the courtyard and the final battle, I regressed roughly two hours back in the game. Suppressing a heart attack, I went through it all again and managed to beat the Queen the second time around. Needless to say, that soured the experience of that otherwise delightful game for me.

I was playing Darksiders today and had a bit of a glitch.

I was in the second "dungeon" in a room with a bunch of decorative pipes on the wall. I was fighting a group of enemies with a weapon which sends people flying and after I had killed them all the doors did not open and I was stuck.

I started to use the lock on to try and find a wayward enemy I had missed and eventually saw one about ten feet in the air with his head stuck in the L-curve of one of those pipes. He was upside down, held perfectly still in the air so that he almost looked like a piece of the environment. I threw my glaive at him a few times until he exploded and I was free to continue, but it was a rather funny glitch.

A favourite of mine is the Goldeneye "Get Down" glitch.

Here's a link to a Youtube video showcasing the bug--set to awesome music just like the Skate and Assassin's Creed vids!