For some unknown reason I am completely fixated with glitches. I get giddy when I pass through an invisible wall or get to a place I'm not supposed to. It makes me appreciate the game a little more.
When I found a way to get out of the game boundaries in Saints Row, I started playing it constantly again, despite the fact I finished the game completely and surpassed the "fun" available in the game. Seam-walking in Ocarina of Time gave me more enjoyment than playing the game did. I don't know why, but I actually like it when a programmer "slips" up and lets a glitch through.
I get to see the tricks they use. The methods they utilized. The way they created the world I inhabit when I play. Seeing the floating Hyrule castle was great, and the 2D image of the town was funny as hell. Exploring Rainbow Six Vegas' maps a little more (online with friends only, of course) was entertainment at it's best.
Of course, glitches cause problems as well, and when these glitches make it onto the online audience it can get ugly. But either way, I will always find ways to get to that little spot that you can't get to.
What's your favorite videogame glitch?