Screw the haters, PSP is a good system, its main letdown is only having the one analogue stick but otherwise I think it's great fun. Also yeah it DOES have games, some pretty decent ones.
Monster Hunter Freedom Unite
Dissidia Duodecim: Final Fantasy
God of War Chains of Olympus
Extra stuff: Ace Combat Joint Assault, God of War Ghost of Sparta, Castlevania collection, Metal Gear Solid Peace Walker, Tekken 6, Silent hill origins, Gran Turismo, Burnout Dominator, Wipeout Pure, GTA Liberty/Vice City Stories, Metal Slug Anthology, Ultimate Ghosts n Goblins.
I haven't mentioned any JRPG's there (Dissidia doesn't really count) even though I'm a massive fan of them, as per your request OP.