Buffy the Vampire Slayer:
Well done game, even for those who don't like the series. You can do a spinning kick to a vampire, send him flying back into a wall, grab a pool cue, and stab it into his heart and see him turn to dust. Can't get much better than that.
Halo:
This was is a no-brainer. It is the first, and best reason to own an Xbox. The only thing that will overtake it is Halo 2, where you can use it with Xbox Live!
Splinter Cell:
If Halo is the best reason to own an Xbox - then Splinter Cell comes damn close. The shadows... the gadgets... the whole spy genre done right.