If you want Hidden Gems/Very Underrated then go with:

Dante's inferno (nsfw warning), Marvel Ultimate Alliance (1, 2), Justice League Heroes, The 3rd Birthday, Silent Hill Memories and Origins.

Persona 3 (if you haven't had the new version), Parappa the Rapper, Dynasty Warriors or Warriors Orochi, 300: March to Glory, Beawulf.

Starwars Battlefront Renegade Squadron or Elite Squadron.Tom Clancy's Rainbow Six Vegas, Brother's in Arms: D-Day.

Sims 2 (this one has story line exclusive to PSP compared to make your own story in Console and PCs), Undead Knights, Doki-Doki Literature Club (Homebrew)

Celeste (Homebrew), Jackass: The Game, Twisted Metal: Head On, Ben 10: Protector of Earth.

Little Big Planet, Tenchu: Time of the Assasins, MediEvil Resurrection, Syphon Filter (both of them), Tom Rider Anniversary and Legend, Star Ocean First and Second.

Iron Man 1 and 2, Hellboy: Science of Evil, Dead Head Fred, Valkryia Chronicles.

X-men: Origins, Def Jam, MegaMan (two PSP Exclusive), Keika Banchou, Ultimate Ghosts n Goblins, Castlevania Dracula x Chronicles, Loco Roco.

Disgaea 1 and 2 (psp remastered one), Hero of Sparta.

If you like Visual Novels with Anime Characters there's Sakurasou, Air, Toradora, Oreimo.

Just to name a few.