Contra 3: the alien wars emotion_donotwant oh wait this isn't snes?
Fine,360 games then. emotion_awesome
Borderlands 2 <----- a rpg+fps hybrid that will blow your freaking mind
left4dead 2 <--- zombies galore+horror survival
deadspace 2 <--- horror survival with creatures
dead rising 2 <---- zombies galore and fun sandbox game if you want it to be
Favorite games for the 360, in no particular order beyond the first...
*=Exclusives (last I checked)
Sega All-Stars Racing
Left 4 Dead 2
Kingdoms of Amalur
I hear great things of Borderlands (1&2) and the Mass Effect series but I've yet to play them, and a lot of people adored Deadrising (the first one) and Brutal Legend, but I didn't care for either one... though BL is totally fun to watch someone else play.