So far, all the REALLY good ones have already been mentioned. But here's my opinion:
Trails in the Sky is great and needs the support so we can see the 2 sequels come state-side.
Persona 3 Portable is wonderful if you have 70+ hours to kill. Haha.
Riviera is a fun little short game.
Ys Seven was the best game I personally played on the PSP.
Final Fantasy 4: The Complete Collection if you want a BUNCH of great nostalgia.
And 2 turn based RPGs that I particularly enjoyed that weren't mentioned yet are Crimson Gem Saga(a fun, although pretty challenging game) and Hexyz Force(a fun and pretty damn easy game).
Yup, that's all I can come up with at the moment. I hope you find a good one!