Well, since my rig is a bit old, I dont have any opinion about the newer fantastic games.
Here's my list:
Mafia (Best Game you'll ever play, very much like GTA)
Hitman 2( You can't win this game without strategy, unless of cheats ofcourse.)
Call of Duty( Real action-packed game, but not like the "Just-Shoot em up type)
Fifa 2005 ( The Best of Fifa series so far)
WWE Smackdown Here Comes the Pain (PS2)
Counter Strike ( Adds to the fun if you own a fast Internet Connection )
Splinter Cell 1 ( Needs no intro.)
GTA Vice City ( Everybody wants to own it )
Age Of Mythology ( Very similar to AOE, but much better )
Max Payne 1 & 2 ( Very strong Story line supported by some greatest FPS you'll ever experience.