Dead rising (amazing sandbox game, tonnes to do)
Project gotham racing 3 & 4 (3's better though)
Rockstar table tennis (good online multiplayer and fun)
Ninja gaiden 2 (underrated, great hack and slash and cool obliterations)
Saints row (good GTA clone)
Smackdown v raw 07 (better than 08 by a mile and still played online a lot)
Crackdown (good sandbox type game, super human jumps, 2 player online)
Halo 3 (better than some say, online is brilliant, 4 player co-op story)
Condemned (way better than condemned 2 and cheap now)
Ace combat 6 (take to the skies, online multiplayer too)
Prey (underrated FPS, and online multiplayer)
Forza motorsport 2 (good solid racer and good online, realistic damage to cars)
Quake 4 (comes with Quake 2 on a bonus disc)
Lost odyssey (amazing game)
also consider either virtua fighter 5 or virtua tennis 3 because both games have online multiplayer on the 360 and are still played by lots of people
Xbox live arcade games (the following all have online multiplayer).......
Streets of rage 2 (best side scrolling beat em up of all time)
Ultimate mortal kombat 3 (after 2 years i still find opponents within 30 seconds)
Ikaruga (amazing old school shooter, one of the best)
Rez HD (simply brilliant game)
Doom (absolute classic FPS)
Golden axe (only 400 ms points for this classic? bargain)
and one more game but no online multiplayer.... Soul calibur (AMAZING)