The lights are on
It depends on what you're looking for in a game. Role playing? Shooters? Sports? Single player? Multiplayer?
Best answer for you is to go on Xbox live and try out their large array of demos to see what you like before you pick anything up.
But if you're looking for straight answers, single player solely i'd have to go with Fallout 3. Bioshock, Fable II, Lost Odyssey, Mass Effect, Assassin's Creed.. Although i haven't had a real chance to play it "Alone in the Dark" seems like a good game (correct me if i'm wrong).
Multiplayer i'd go with well any new release sports games, based on your preference, because of the amazing way developers have handled online updating to match real life games and seasons. Call of Duty 4, and if you want the most challenge online hold off for Modern Warfare 2.
Also the original Gears of War was also a good single player game and had a great team-based multiplayer, but hard to tell if anyone really plays it online anymore.
I could go on and on, but those are a few of my personal favorites, hope it helped you with any decisions.
Edit: Also look into Brutal Legend, new game based on a highly "Metal" world. Right off the bat, you can see how graphic the game is, in language and violence, but Jack Black does a great job voice acting, and kept me highly entertained as i was hacking through demons.