When just playing a game isn't enough...

Super Mario Bros. collision detection bug

Meqon GDC 2005, ball jumping bug

Half-life speedrun with various bugs/exploits

Fable money bug

Guild Wars collision detection bug

Speed collision detection exploit in over 90 degree corners, that let's you noclip through walls

World of Warcraft, world changing exploit (done on normal servers),
Exploration the Movie and Nogg-aholic the Movie

This list is only a small fraction of all the bugs/exploits I've encountered during my years of gaming and be sure that it will eventually extend even further.