Carmageddon!!!! Complete with soundtrack by Iron Maiden.
Ok, so it's a PC game, but it would be right at home on consoles. It game makes Grand Theft Auto look like Candyland. For those of you who haven't experienced the awesomeness of Carmageddon (Carmageddon 2 was the best), it's basically a racing game/auto combat game. The races take place in HUGE outdoor environments that can be explored freely and are full of secrets. You race through a series of checkpoints, but you can get to them however you want, rather than following a track.
Of course, if you don't feel like racing, you can just kill all your opponents. The car selection looks like it came straight out of Twisted Metal. You can upgrade them or buy new ones with money earned from racing. There aren't many projectile weapons, though. The emphasis is on smashing your opponents into things or knocking them off cliffs. If you plow your opponent into the corner of a building or something, you could even slice their car in two.
The best part, though, is that this game gives you money bonuses for causing random destruction wherever you go. You get money for hitting civilians (supposedly they were turned into zombies or something. . . whatever), deer, elk, and really anything else that moves. You get bigger bonuses for hitting them so hard that they dismember, or you can get the pancake bonus by plowing them into a wall. There are powerups like the spring weapon, which automatically launches springs at any civilian within a certain radius of your car, sending the little rag dolls flying way off into the distance.
P.S. Weren't they making a Destruction Derby game for PS2? What ever happened to that?