Time Splitters Futur Perfect for its huge range of customisation options making levels etc.
killzone 2 for its graphics, amazing on HD PS3
online console ofc it has to be Halo and Cod (4 over 5)
the First Cry though quite old (so the graphics etc aren't much now days) is a great shooter game (and as its ubisoft the top difficulties are incredibly hard)
CoD4 is awesome for it graphics and multiplayer. The story line is good and can be played a few times. The prestiege is also a nice way to give the multiplayer some depth.
Killzone 2 is also another great FPS. The graphics are down right amazing. Has a great story and makes you wait with anticipation for the third one. The mutilplayer is also great because of the use of badges with special abilities along with massive levels and teams.