Top Gear Rally on N64 had strange physics with rails around certain corners: you could slam into the rail and turn with it, accelerating the whole time. On the Quarry course, this allowed for super speeds and quick times. My friend and I spent heaps of time posting time trials with this method.
Halo 2 was all about glitches for me. Because of how crazy they were, it really just let my imagination run wild. A lot of my time playing the game was just trying to learn them or find new ones.