Persona 3 Portable is my favorite portable RPG ever. Great story, 75+ hours of gameplay easily. Phantasy Star Portable and the sequel are also really fun if you can overlook a cheesy plot for fun gameplay.

Classic Game Room - PHANTASY STAR PORTABLE 2 for PSP review - YouTube

I want to play Phantasy Star Portable again.

EDIT:

Oh I forgot to mention. You can play the online with others in Phantasy Star Portable 2 on a rigged PSP. I forget how but I was able to do it with a bit of tweaking as long as I didn't host.