Overall Favorite:
Carcassonne. If you want to play online, check out
this guide I wrote.
Best Strategy: Skulls of the Shogun. Has a nice cross-platform, asynchronous multiplayer mode, and also a good single-player story.
Best Puzzle: Hexic Rush: A unique twist on the genre with two very different modes that freshen things up, plus the Xbox achievements are challenging, but fair.
Best Sports: NBA Jam. Unfortunately the multiplayer is spotty (I never got it to work), and the achievements are a grind, but overall, this game is still a blast.
Best Word: (tie)
AlphaJax, Wordament. Alphajax is like Scrabble; Wordament is like Boggle.
Best Retro :
Rocket Riot. A blast to pick up and play for a few minutes at a time.
Best Shooter :
Halo: Spartan Assault. The controls on this game are fantastic, the graphics are top-notch. It's a blast.
Best Platformer :
Mirror's Edge. A really cool side-scroller with fantastic music, great presentation, a good story, and intuitive touch screen controls.
Bonus: here is a
list of multiplayer games I've compiled.