Mobile Suit Gundam Zeonic Front - Only if you like Mechs and Rainbow Six type tactical shooters - it's very different from any other Gundam game
Kingdom Hearts 1 & 2 - Fun action hack and slash rpg, cute cuddly, disney and final fantasy, great games
Persona 4 - JRPG, good story, great characters
Final Fantasy X - some questionable voice acting is raised against it, but it has good character class based mechanics, a slight pain in the ass upgrade system but can be used to customize characters to player's discretion
Final Fantasy X-2 - Heavy Note on X-2 most people hate it, but if you can forget the story, and the characters being turned into empty headed dumbasses the gameplay and mechanics are really good
Final Fantasy 12 - a slightly less standard JRPG for FF with a more real time combat feel - ofcourse only if you like JRPGs for those last ones
King of Fighters XI - only if you like Fighting Games
TimeSplitters 2 or Future Perfect - FPS with goofy characters, future perfect for a better story line, but I prefer 2's levels
Twisted Metal Black - Online or whatever the edition is called is rated T, standard edition is M - if you don't know twisted metal
Project Eden - a FPS/TPS team based game, can be played through the story with anywhere between 1 and 4 players, puzzles can be a bit of a pain, but fairly fun and I barely ever hear about it from others
Armored Core - if you like mechs only
edit : anything Ratchet and Clank also of course
Rated M
anything Resident Evil, Silent Hill 1,2,3, anything Fatal Frame - if you like Survival Horror