Assassins Creed - this will keep you busy for a long time.
Grand Theft Auto IV (coming out early 2008)
Ninja Gaiden 2
Other than that, do you have a PS3?
If you did you could try Rachet & Clank, Uncharted: Drake's Fortune, those are great games and there are many more.
Not that I'd be much help since I don't have a 360, but I do read way too much video game news. The Elder Scrolls IV: Oblivion has been out for a year and a half but has a 9.6 score on gamespot. I think there is a thread on here about Assassin's Creed, too. Definitely not your run of the mill FPS.
Here bud, Xbox Games List (Xbox 360) By Genre
Just chose Action/Adventure on the scroll down menu, you should get a complete list of the games that are action/adventure, after that I would go to Google and read some reviews on it.
Good luck, hopefully it helped.