1) Bioshock
2) Fallout 3
3) Red Dead Redemption
4) Raiden Fighters Aces
5) Brothers In Arms Hells Highway
6) Gears of War (series)
7) NFS Most Wanted
8 ) Left 4 Dead
9) Conan
10) Dante's Inferno
The usual A-List titles that are universally praised, but some others that I just had a complete blast playing multiple times. Need For Speed Most Wanted and Gears of War were the games that pulled me into the 360 initially way back in 2005. I saw the high resolution graphics and I just had to have this new console. It also had HDMI output, so the 360 truly was a big step in gaming on the visual side, and not just in more polygons, but in the actual clarity capabilities.
Conan is a sleeper hit in my opinion, it's my favorite hack n slash. I know some say Dante's Inferno is just a copycat of God of War, if true then so be it, but I like the Crusades as the backdrop, and descending into the 9 circles of Hell, the game puts on an amazing atmosphere with some really creepy moments.
Brothers In Arms ended up being my preferred WWII game on the system, and I played all the CODs.