Must have games for the 360 would have to be:
Halo 3 +2 + 1. -Halo 1 = best game ever made, Halo 2 = best multiplayer halo 3 = well, halo 3.
Gears of war -1, aparantly No. 2 is shithouse online, both campaigns are top notch
Call of duty 4 - Very good multiplayer, can also get COD5 if your so inclined.
Forza2 - Car simulator, better than GT, Full bodykits, full paintjobs, drifting/time trials/endurance races/everything. $15
GTA4 is also good however i didn't think it was that good, was so shocked to see it get 10/10.