Recent great Xbox games are:
Advent Rising- (a lot of people don't like this game, but it has an excellent story, superb music, and the pacing of the game is top notch. There are major problems with controls and frame rate though.)
Forza Motor Sport
Doom 3
Mech Assault 1 & 2
Some older games are:
Halo 1 & 2
Shenmue 2- (its kind of a slow paced game, but the story will most likely keep you interested.)
Cronnicles of Riddick
Full Spectrum Warrior
Crimson Skies
Steel Battalion- (it cost an arm and a leg though)
Dead or Alive 3 & Ultimate
Ninja Gaiden
Otogi 1 & 2
Star Wars Republic Commando
Panzer Dragoon Orta
Moto GP 2
Future games:
Far Cry Instincts
Half Life 2
Moto GP 3
Fable Lost Chapters
Time Shift
Pain Killer
Hope that helps.