What type of genre games do you like?
I like strategy myself. 2 good ones that are psuedo-real time (in that the game plays in real-time, but you can pause it to issue orders) are Hearts of Iron II, Knights of Honor. I've had a lot of fun with HOE II - you can play any country during the WWII era, and not just the big ones. Those are both PC based games.
And sports - you really have to have some version of Madden football. It is out on all platforms. Madden '06 really isn't much better than '05 though, and you can get '05 really cheaply.
Another genre you might consider is the "dance" game. Laugh, but it is extremely addictive, and manages to give you a workout while you play. For X-box, i'd go with Ultramix 2. On PS2, I'd start with DDR Max 2 (if you've never played before), or In the Groove if you already know you like that type of game.