I have a decent collection on PSP games and I suggest
Metal Gear Acid - It may not be for everybody, but I was really into it for a while.
Hot Shots Golf: Open Tee 1/2 - They are really fun games!
Ratchet and Clank: Size Matters - It's not a very long game but there are plenty of unlockable weapons with tons of upgrades. It is a good adventure game.
Resistance: Retribution - It is a pretty good shooter game, and the story and everything is good too.
Castlevania: Dracula X Chronicles - I didn't care much for the main game but you can unlock Symphony of The Night which is an awesome game.
I think all the games listed are less than $20 except Resistance.