Perhaps if you tell what you enjoyed on previous game systems we can make better recommendations?
Gran Turismo 3 is the best car racing game out there; its so real looking that I've had people walk by the demo mode and think it was some motorsport on ESPN. Drives good, looks good.
I played Onimusha and was pretty frustrated with it. I remember sitting through interminable movies and cut-scenes in order to get a few seconds of game-play. It looks great though, and it is slightly more interactive than Dragons Lair. ;-)
Dance Dance Revolution is a huge hit and a fantastic party game; although the idea of actually dancing to play a game may turn some people off. Dont bother playing this with just the controller; its only fun with a dance-pad.
Grand Theft Auto 3 is a big hit, but, be warned, it is rated M for Mature. I havent played it personally, so I cant say how far it goes, but I do remember thinking Kingpin had crossed the line. Considering that I think Quake is the greatest thing since sliced bread, I dont consider myself a big wuss on violent content.
I played Max Payne on the PC and enjoyed it a lot. The gameplay gets a bit repetetive, but its really well written. Imagine that -- a shooter where the story actually means something. Beautiful over the top noir. Pretty violent too (its key gameplay feature is "bullet time" where the action becomes John Woo style slow motion), but theres a point to everything that happens.
