Forgive me for probably repeating stuff that everyone else has already said.
-Devil May Cry 3 (Get the special edition or you're going to be throwing your controller at walls)
-The Splinter Cell games
-Silent Hill 2 (although I'd recommend the Xbox version if you already have a 360... just don't make more than one save file or the backwards compatibility will crap itself). I can't speak for SH 1 or 3, but I really don't think 4 is worth your time if you have a bunch of other games to be playing.
-If you can forgive stupid plot points, annoying characters, and truly irritating combinations of the two for the sake of fun combat and tight gameplay, get the Kingdom Hearts games.
-If you can forgive somewhat (not cripplingly, but it is noticeable) shallow game design and you're a fan of the Castlevania series, I'd recommend getting Lament of Innocence (although you'll need to visit GameStop to get it) and Curse of Darkness.
-The GTA games.
-I've never played RE4, but everyone and their cat tells me it's excellent, so get that I guess.
-The God of War games.
If you're also looking for PS1 games, regardless of whether you like Castlevania or not, get Castlevania: Symphony of the Night if you can (it's pretty rare, but worth playing if you can find it). Skip all the 3D Final Fantasy games though. The only ones worth your time are 4 and 6.