The PSP was such an unpopular system, but almost all of my console gaming has been on that system. If you want you can look at my GameFAQs reviews and look into anything you don't recognize.
In particular, I'd like to recommend Cladun and Shadow of Destiny.
Cladun is an action dungeon crawler. The levels go well beyond the final boss and reach an absurd difficulty, which is cool. You also do most of your grinding in randomly generated dungeons with adds a lot of replay value. The big seller in Cladun is the way the game manages stats, which happens through a suped up Materia-like system that allows you to equip stat boosts. However, if you take too much damage from one side (front/rear/left/right) you lose the character who has equipped said boosts and lose the benefits. Character management is extremely deep and there's a surprising amount of variety.
Shadow of Destiny is the total opposite in terms of game experience. It's practically a visual novel in that it barely has any difficulty or even gameplay, but the storyline is incredible. You play as a character brought back to life to prevent his own death using time travel. There are some corny moments and instances of bad voice acting but at the center of all the smoke and mirrors is an EXCELLENT title. The amount of twists and turns in the game are unprecedented, and each of the 8 endings reveal different spoilers about the game, so replaying it is more rewarding than just seeing different characters living or dying at the end.