This list is by no means definitive, it is merely my favorite RPGs on the PSP. If you don't like it, just remember that. If you have any suggestions for games I should include, comment away!
Top 5 PSP RPG titles:
1- Final Fantasy: Crisis Core
I don't like that Crisis Core is the best RPG on the PSP. Because it's a dying franchise, and it's really 'mainstream' to put a Final Fantasy at the top of the list. However, it's easily the best game on the PSP. The graphics are top notch, the combat is brilliant, and it's got hours of content. It is a healthy prequel to Final Fantasy 7, that anyone can enjoy. Even though I didn't want to put this at number 1, there's no doubt in my eyes that it deserves the spot.
2- Shin Megami Tensei: Persona 3 Portable
When I came across Persona 3 sitting lonely on a shelf, I bought it without a second thought. It was a brilliant game for the PSX, and it's even better on a handheld. It's got a great story, that can't be fully experienced in a single playthrough. The combat is challenging, demanding that you climb up over 200 floors of enemies in under a year. Persona 3 Portable is basically tied with Crisis Core for first place.
3- Kingdom Hearts: Birth By Sleep
Birth By Sleep is the best handheld Kingdom Hearts game. It has addictive and layered combat, a brilliant plot, and 3 separate characters to play the story with. The only shortcoming this game has is that it's too short. That and the Disney part, which I'm okay with. Even if you know nothing about the Kingdom Hearts universe, this game is still worth playing.
4- Valkyrie Profile: Lenneth
I hated this game at first. It was overly complicated, without much explanation. 5 hours later, I was balls deep in dungeons, recruiting new characters and perfecting them before I could toss them up to Valhalla. Although it has a patchy plot and is difficult to pick up, Valkyrie Profile is yet another game from the PSX that made a wonderful transition onto handheld.
5- Star Ocean: First Departure
I've always liked the Star Ocean games, they've been a solid RPG over the years with less appreciation than deserved in the west. First Departure brings some of that old school spice onto the PSP. The combat is a little basic, but the story and the characters are amazing. You can't recruit every character in one playthrough, and there's loads of side content to complete. I really loved grinding on this one.
If you're looking for PSP games, this list might help you. The PSP almost has more RPG titles than I can buy, but I will keep on purchasing the ones that I can. Feel free to comment if you have an opinion on your favorite PSP games!