The psp, for me is the best handle console ever made (yes better than gameboy etc, are my likes ok xD ) and one reason for it is because of the rpg selection. For me the best rpg selection that you can come by after ps2 rpg games of course.
I will make my list by category (action rpg, turn based and tactical) and also maybe I will have some left because I dont own or never played them
Turn Based:
Brave Story (for me the best game of the console)
Hexzy Force
Crimsom Gem Saga
Valkery Profile
Tales of the world (there are more tales of games but are in jpn)
Legend Of Heroes (the are like 3)
Monster Kindgom Jewel summoner (Pokemon style with dragons)
Dragoneer's Aria
Final Fantasy 4 (there is also ff3 jpn only)
Fate Extra
Persona games (1, 2 and 3)
Action Rpg
Final Fantasy 7 Crisis Core (the best action rpg) (also type 0 is good but is in jpn :/ )
Tales of Eternia (another really good tales of game)
Monster Hunter (this game is the reason that the psp came way popular, everyone was playing it back then, there are like 3)
Kindgom Hearts
Gods Eater Burst
Lord of Arcana
Ys games (there are like 3)
Phantasy Star Portable and 2
Blade Dancer
Star Ocean (the first and second one)
Dudgeon Explorer
Valhalla Knights and 2
Tactical Rpg
Jennae D'ark ( the best one)
FF Tacttis
Valkyria Chronicles II (tactical shooter)
Wild Arms XF
Yggdra Union: We'll Never Fight Alone
Generation Caos
Ragnarok Odessey
Astonishia Story
Mana Khemia: Student Alliance
Blazing Souls Accelate
Class heroes
Dissgaea (the are like 3 games)
Half-Minute Hero
Knights in the Nightmare
Phantom Brave: The Hermuda Triangle
Riviera: The Promised Land