Thrill Kill for Playstation. (wikipedia can be found
here) It was canceled prior to its release but my cousin had a mod chip and got it off the internet. Me and my cousins played this sh*t for hours on end. Really, really fun despite what Gameinformer said about it. At the time the violence was unprecedented so that was cool to see but it was also a really fun and unique fighter game, awesome multiplayer. Here's an article about the game from IGN:
<div class='quotetop'>QUOTE </div><div class='quotemain'>Gameplay is very different from the standard fighting game. First of all, it's more of a party game in the sense that four people can play the game at the same time. Once the match begins, you'll be punching and kicking, but there's no dmage. Instead, you've got this powerup meter that increases every time you punch, kick, or combo someone. Once that meter's filled, that player can now kill for a short period of time. They get a really impressive powerup, then go after another player. This is the cool part. When the other three players are scrambling to get away from the killer, they have a special move where they can throw an unlucky opponent into the path of the killer player. Should a character get killed, you're treated to a very, very gruesome fatality. For example, the maid can grab a person's head and slice it off, at which point the body spurts blood and the head goes flying, also gushing a bright red fountain. Then it begins again, with one less character. The last kill gets an extra special death animation, called the ThrillKill and that's where the game gets its name.</div>
http://psx.ign.com/articles/123/123823p1.html
Also maybe its more popular these days but I also played GTA 1 and 2 a ton with my cousins as well long before GTA 3 came out. Kind of funny looking back on that crappy birds eye view thing but it was good times.