I remember Destruction Derby! I didn't play it much, but yes, the racing part was not what the game was for.

Need for Speed III was actually the racing game I played the most on the PS1, and I think is the first of BoB's list that would have almost certainly been in my top 100 too. My friends and I played that thing for hours. We even found cheat codes to unlock some ridiculously fancy and fast cars and enjoyed absolutely blazing through the different areas. I think NFSIII was the first in the series to introduce the cops, and that added an additional fun level of gameplay over your typical PS1 racing game. I never played much more of the series after that, though I did play a bit of a more recent version on a friend's PS3 a couple of years ago, which was pretty fun.

Pike: were you talking about NFSII or NFS: Hot Pursuit 2? I don't think I ever really played either, but they are different games.