I have a xbox 360 and a wii and I'm going to have to cheat since all these games deserve mention.
Xbox 360: Bioshock
The atmosphere created by the graphical design and the sound effects combined with the story make Rapture one of the best and most memorable settings ever in a videogame.
Runner up: Mass Effect.
The guys at bioware return with not only a great RPG but also one of the best pieces of Science Fiction entertainment in recent memory.
Wii: Super Mario Galaxy.
This games brings back memories and extends the limits of the unfortunately dying platform genre beyond our wildest dreams at the same time.
Runner up: Metroid Prime 3: Corruption.
Finally the wii-mote works perfectly. Add great graphics (for the wii that is) and challenging boss figts and you've got one of the best games this year.
GAME OF THE YEAR: Super Mario Galaxy.
Did I mention that it's Mario, that it has some of the best level designs ever and that it's probably the best platformer ever.
Runner up: Bioshock
It's one of the most remarkable and memorable games in recent history no doubt about it but the gameplay could have been better.