Dragon Age: Origins: Another medieval fantasy RPG influenced by Game of Thrones. To the point that it's about a kingdom that needs to repel a zombie invasion but is too busy fighting amongst itself. Also it spells "sir" with an "e".
Pretty standard plot; you're recruited to an elite fighting force, something goes wrong and you have to pick up the pieces. It's a BioWare game, and the gameplay is like Knights of the Old Republic with Final Fantasy 12's combat support system.
I enjoyed the hell out of it (and the expansion, Awakening, was pretty good too) but never got around to playing the sequel, which I hear is a much different game and which got pretty mixed reviews.
Ghostbusters: The Video Game: As a game it's okay. As a Ghostbusters sequel, it's great. They managed to get basically everyone from the movies except Sigourney Weaver and Rick Moranis back together; it's funny and it makes for a great continuation from the movies.
Do not confuse it with Ghostbusters: Sanctum of Slime. I haven't played that one, but it doesn't have the actors from the movies in it, and from what I've read it's terrible.
Mega Man 9: Another downloadable game. It's a new Mega Man game in the NES style. Think of a game as complexly designed and bitch-ass hard as Mega Man 2 or 3; now think of it with 20 years' more of game design knowledge attached to it. (There's a Mega Man 10, too; it's neat but not as good as 9 and I never did get around to finishing it.)
Also, I've started Gears of War; I haven't gotten far but it seems like a damn decent cover-based third-person shooter. And I got it for under $5 used. I also enjoyed the demos I played of Fez (a puzzle platformer based around rotating a 3D world that you can only move through as a side-scroller) and Pac-Man Championship Edition DX (which is a new Pac-Man game with different maze layouts, slightly different play mechanics, and a whole lot more ghosts -- another retro-style game with a really good modern design sensibility). The neat thing about all the downloadable games on Xbox Live is every single one of them has a demo you can download; given sufficient bandwidth and a hard drive you can try out a few levels of a new game or three every day and enjoy the hell out of just doing that.
Other games I haven't gotten around to playing but hear are good: Dead Rising, Bioshock, Skyrim, The Orange Box, Bayonetta.
I started a thread called Xbox 360 101 over at brontoforum.us; it's full of various recommendations.
So there ya go -- more games than you can shake a stick at and probably more than you can find time to play. That's like 5 years' worth of games for me, even though I just got my Xbox six weeks ago, since I played most of these on PC.