What is a good game for xbox 360

There are a lot of great games for the 360. It'd be easier to find what game to suggest if you told us your favorite genres.

Since you didn't provide that info, I'll just post some favorites according to genre. But please, next time you ask a question like this, tell us what type of games you like. It makes things a whole lot easier.

JRPGs:
Blue Dragon
Eternal Sonata
Lost Odyssey
Tales of Vesperia

WRPGs:
Fable III
Fallout: New Vegas
Mass Effect 2
The Elder Scrolls IV: Oblivion

Fighters:
BlazBlue
Marvel vs. Capcom 2: New Age of Heroes (XBLA)
Soulcalibur IV
Street Fighter IV

FPS:
Battlefield: Bad Company 2
Call of Duty: Black Ops
Call of Duty: Modern Warfare 2
Halo 3

TPS:
Gears of War
Gears of War 2
Lost Planet 2
Resident Evil 5

Platformer/Sidescroller:
Alien Hominid HD (XBLA)
Mega Man 9 (XBLA)
N+ (XBLA)
Shadow Complex (XBLA)

Of course, there are more genres than these and many more games to recommend. Hope you find one you like. ;)