too many good games from so many genres that it's hard to pick a "best game"
FPS:COD2 - one of the most forfilling single player experiences I've ever had in an FPS. playing through on Veteran was insane and made me fall in love with the series. I've heard it's awesome online though I've never played.
GRAW - Amazing Graphics, Amazing gamplay, Amazing amount of options
Prey - Simply awesome graphics and mind-bending level design. Fast gameplay definitly brings FPSs back to their Doom and Quake ROOTS. online play is hit or miss just be sure to host all your game or do a custom match and pick one with a good connection speed.
Fighting:DOA4 The best DOA game to date, drop dead graphics, awesome twitch gamplay and more online options then you'll know what to do with. Online play is virtual lag-free and some of the best around
FNR3 Quite possibly some of the best looking graphics of any game... ever. Really unique gameplay for a boxing game, and lots of options to keep you playing.
Street Fighter II it's on the Xbox Live Arcade... it has online multiplayer... need I say more.
RPG:Oblivion if you had to choose one game as the only game you could play for the next 4 months... choose this game. MASSIVE isn't a big enough word to describe it. Some of the best graphics the console has to offer so far and oodles of game there to play.
Final Fantasy XI A lot of people here don't like it but there is no denying that it's one of the biggest and best MMOs on the market today, with graphics comperable to that on the PC and the fact that you can play alongside the PC and PS2 players is reason enough for any MMO fan to pick this up. It's also aparently one of the more popular 360 titles despite the negative attension XSers give it.
Action/Adventure:Condemned wins my prize as my favorite game on the console so far. AMAZING story, awesome graphics, unique gameplay, and just a really creapy game in general. Anything that can still give you the chills the 2nd play through certainly ranks as a scary game in my book.
Kameo Awesome graphics, really unique gamplay and very reminisent of the fantastic platformers we all know and love from the N64.
Tomb Raider Awesome graphics, classic gamplay that will remind you of a cross between the classic TR games and Prince of Persia sands of time. Plus enough hidden stuff to keep you playing for a while
Racing:PGR3 Awesome graphics, buttery smooth gamplay, tons of amazing real cars and location, a track bulder to make your own custom routes through REAL cities, more online options then you'll know what to do with, not to mention I've never once EVER experienced lag with this game online... it seems to just be non-existant. If you're a dedicated racer there are always tournaments going on as well.
Burnout Revenge One of the most fun arcade racers I've ever played 100s of options for both online and offline gameplay both this and PGR3 will take you months to complete... if you ever complete them at all.
XBLA:Geometry Wars I think that you should be required to buy this game if you own an Xbox 360... it's $5 and you should own it... that's all you need to know.
Marble Blast Ultra Remember Marble Madness... now make it 100 times more interesting, give it amazing graphics and realistic physics, a multiplayer mode, and charge only $10... now go buy it
Other:R* Table Tennis A simple game but stupid fun... it makes table tennis as fast paced and technical as a top knotch fighting game
Chromehounds Build a completely custom mech and take it online where you'll partake in a full-scale world war between continents... wars last weeks and have real players in real time on all sides of the battle field.
... do you need me to keep going?
this isn't the Xbox 1... there isn't just Halo and then everything else. There are a lot of games in a lot of genres that are a whole lot of fun.
If you're interested to see what people are playing RIGHT NOW check out the game tracker on mygamercard.net
http://www.mygamercard.net/tracker.php