That's a huge matter of opinion
There's alot of games I love on the 360 but it's too hard to pick just one
Halo 3, Call of Duty 4, and Gears of War are games that I played alot online and offline. Of those three it's a close tie between Halo 3 and CoD4, but too hard to pick.
As for single player games, I loved The Orange Box (Half life games), Bioshock, Oblivion, Fallout 3 and Mass Effect. I played Mass Effect twice and that includes beating it 100% (all side quests). Of those three my favorite was Mass Effect.
In conclusion... it's a matter of opinion and just too hard to choose.