My first game console was the Nintendo Entertainment System. I didn't use it much, but I just had a few Mario games for it.
Then in 1997 I got the original Playstation, which I used heavily from 1997-2004. I had tons of games for it, but my favorites included Vigilantie 8 (sp) and the Driver series (1 and 2). I sold the PS in 2006.
In early December 2002 I got a Gamecube from a bowling league. I never used that system much and is currently just sitting unplugged.
In June 2005 I got an Xbox, just months before the Xbox 360 came out (I guess I should of just waited a bit longer hehe). The games I play on there include Driver 3 and Burnout. I plan to get the fourth Driver game soon. According to Wikipedia, the game is available on Xbox, but I don't see it in any store (retail or online). All they have are PS2 games.
I also have played a few computer games, but I have always used game consoles more mainly because I have used Macs all my life until two years ago and not many good games are available for Macs.