CALL OF DUTY 4: MODERN WARFARE
BATTLEFIELD: BAD COMPANY
CoD4 is freaking addicting...proceed with caution. or you'll be like 'one more game...' and before you know it, the sun will be up...
Battlefield: Bad Company is huge, also addicting once you get into it, i just don't like some of the maps in it...and there's lag in the new ones, which kinda ruins it. CoD4 is definitely worth every penny though. hell, get them both. bbc is $30 and i think cod4 is still $60. world at war doesn't compare to cod4.
i hear left 4 dead is also a good one.
another one i would suggest, but not recommend if it was more than $20, is Ghost Recon Advanced Warfighter 2. it has tons of game modes, but the matchmaking service downright sucks unless you're the host, or are playing with a group of people you know. there are dozens of maps to choose from, there is some really good co-op in it as well.
for non-fps....hmm i dunno, haven't played many non-fps mp games on the 360. maybe soul calibur 4?