i highly recommend:
1.resident evil 4, easily the best re since, ever.
2.socom 3, if you havent been playing this series your missing out + online play is insane. pick this up asap.
3.gta:san andres, im not a big fan of these games but everyone in the world is, so pick this one up to.
4.either you or someone else said EA fifa soccer, skip this and get a game called winning 11 8 (the newest one 9 comes out 2/9). this is the best soccer game ever, its so good it got an award for being the best sports game (beating madden).
5. medal gear solid 3. best mg ever pick it up.
6. god of war. this is another award winning game, it is bloody + great graphics + awsome story = game of the year 05.
7. the prince of persia series, yep the whole thing, whyd you want to jump into the end of a wicked good story. all three are superb.
yeah thats a shit load of games i mentioned, but the great thing about it is most of these games are pre xbox360 release, so there are plenty of used games floating around.