Halo - I have problems with the story of 2, but it's easily the best feeling shooter on a console and playing through the first game alone and in co-op, and online with the 2nd was some of the most memorable gaming this gen.
Psychonauts - Probably the greatest game world/characters. The humor, the characters, the symbols of PSY...it felt like playing through a well done Tim Burton film.
Advance Wars - A little stale at this point, the DS game offers more with far less charm, but playing through the first one on gba was some of the best gaming ever.
Freedom Fighters - I'm almost not sure why, but this setting and easy to use controls make this an extremely compelling action/shoot em up for me. I want a sequel sooooo bad.
Forza - The coolest car sim ever.
Otogi - Not without some major flaws, but so beautiful and odd and strangely satisfying to fight through these games.
It doesn't qualify for this I guess, but the rebirth of the GTA series is simply incredible. San Andreas might be the best game this gen.
This list makes me feel like I liked the Xbox more than I realize. And yet it also makes me fear that the lesser known odd titles that sold like shit on it might not be repeated on 360 and that makes me sad.