I guess I'll chime in and mention some of the XBox v1 games I own and love:
Jade Empire LE
Break Down - Awesome game, in my opinion, that's a mix of Matrix and Terminator for the story that's also more of a first person adventure game than shooter, mostly for the hand to hand combat segments and the feeling of being overly powerful by the end of the game.
Panzer Dragoon Orta - It was mentioned before, but it's an excellent on rails shooter. Plus, it has the original Sega Saturn game as an unlockable.
Dead or Alive 3 - Pretty good fighting game, I find it a bit better than DoA4.
Fatal Frame 2 DC - Again, another game mentioned earlier, but it is definitely worth picking up for the scare factor.
Pyschonaughts - Hilarious plot, great characters, and great game overall. A "definite must have" and often overlooked game.
I'd also mention Halo 2, but that's okay as far as FPS games go.