Take a look at this list. I made it at CAG once and many felt it was a pretty good list (It is missing a few newer games though). Some games are $40, but I want to give you an idea of some good PSP stuff.
RPGs
Breath of Fire III (Euro Import)
Gurumin: A Monstrous Adventure
Monster Hunter: Freedom
Monster Kingdom: Jewel Summoner (I personally love it, but not for everyone)
PoPoLoCrois (I personally love it, but not for everyone)
Princess Crown (Asia Import)
Tales of Eternia (Euro Import)
Valkyrie Profile: Lenneth
X-Men Legends II: Rise of Apocalypse
Fighters
Darkstalkers Chronicle
Guilty Gear Judgement
Powerstone Collection
Street Fighter Alpha 3 Max
Tekken: Dark Resurrection
Puzzle
Bomberman
Crush
Every Extend Extra (short, but fun)
Exit
Lumines
Lumines II
Me and My Katamari (controls are weird at first, but still good IMO)
Mercury Meltdown
PQ Practical Intelligence Quotient (It can be tough, but cool concept)
PQ2: Practical Intelligence Quotient 2
Puzzle Quest: Challenge Of The Warlords
Racers
Burnout Dominator
Burnout: Legends
Outrun 2 Coast to Coast
Pursuit Force
Race Driver 2006
Ridge Racer (or import 2)
Wipeout Pure
Action
Killzone: Liberation
Mega Man: Maverick Hunter X
Mega Man Powered Up
Metal Gear Solid: Portable Ops
Medal of Honor Heroes (some like it)
Socom: Fire Team Bravo
Socom: Fire Team Bravo 2
Syphon Filter: Dark Mirror
Twisted Metal Head On
Ultimate Ghosts 'n Goblins
Flight Shooter
Ace Combat X: Skies of Deception
After Burner: Black Falcon
Platformer
Daxter
Death Jr 2: Root of Evil (not for everyone, but definitely better than the previous one)
LocoRoco
Ratchet & Clank: Size Matters
Tokobot (not for everyone, but fun IMO)
Sports
Hot Shots Golf Open Tee
MLB 07: The Show
Virtua Tennis World Tour
Virtua Tennis 3
Winning Eleven: Pro Evolution Soccer 2007
Music
DJ Max Portable (import)
DJ Max Portable 2
Gitaroo Man Lives!
Strategy
Field Commander
Lemmings
Metal Gear Acid
Metal Gear Acid 2
Sid Meier's Pirates!
Classical Compilation
Activision Hits Remixed
Capcom Classics Collection Remixed
Capcom Classics Collection Reloaded
Capcom Puzzle World (Super Puzzle Fighter II Turbo makes it worth it)
Gradius Collection
Metal Slug Anthology
Namco Museum Battle Collection (IMO, best Namco collection)
Parodius Portable (import)
Salamander Portable (import)
Sega Genesis Collection
Taito Legends Power UP
Twinbee Collection (import)