I never owned a PSP, but tried a few in an emulator. Really missed out on a fantastic device and game library. I think there are some obvious famous games that many recommend, as such

• Crisis Core: Final Fantasy 7
• God of War - Ghost of Sparta
• Grand Theft Auto Liberty/Vice City Stories
• Lumines
• Metal Gear Acid / Peace Walker / Portable Ops Plus
• Monser Hunger Freedom Unite
• Persona 2 Innocent Sin
• Ratchet and Clank Size Matters

Also kind of ports I think, maybe new games in series, I’m not sure. But just able to play these on a portable device is awesome:

• Gran Turisomo
• Littlle Big Planet
• MotorStorm: Arctic Edge
• OutRun 2006 - Coast 2 Coast
• Tekken 6

I didn’t play much on PSP yet. Following are also interesting:

• Ghost in the Shell Stand Alone Complex
• Hot Shots Golf
• Jeanne d’Arc
• R-Type Command
• Tekken - Dark Resurrection
• Ultimate Ghosts 'n Goblins
• WipEout Pure

And the list goes on and on. This was an awesome handheld.