Here's a post I made in this thread: http://vgchartz.com/forum/thread.php?start=50&id=34520
I hate lists, but here's my list of suggested titles:
Racing
Wipeout Pure and Pulse
Shooters
Killzone Liberation
Syphon Filter Dark Mirror and Logan's Shadow
Socom Fire Team Bravo
Sandbox
GTA Liberty City and Vice City
RPG
Brave Story
Disgaea
Final Fantasy Tactics
Jeanne D'Arc
FF Crisis Core
Valkyrie Profile
Platformers
Daxter
Ratchet and Clank
Castlevania Dracula X
Stealth Action
Metal Gear Portable Ops
Action
God of War
Pursuit Force 1 and 2
Action RPG
Monster Hunter
Gurumin
Adventure
Sid Meier's Pirates
Strategy
Field Commander
Puzzle
Puzzle Quest
Lumines
Crush
Echochrome
Music
Beats
Other
Patapon
Loco Roco
These are all highly regarded games according to me, the gaming media, and the PSP community at large. There's enough there to keep you occupied for years. The PSP covers a ton of genres with a good mix of the familiar and the novel. And I probably missed a ton of others.
I highly suggest the stuff listed under Puzzle and below. They're all very unique games, which you seem to be into. Beats is one of the hidden gems that for just $5 lets you play a rhythm music game using songs on your memory stick. 8gb memory sticks are only $65 these days so you can fit a ton of music (and movies).
My Top 5:
Shadow of the Colossus, Metal Gear Solid 3, Shenmue, Skies of Arcadia, Chrono Trigger
My 2 nex-gen systems: PS3 and Wii
Prediction Aug '08: We see the PSP2 released fall '09. Graphically, it's basically the same as the current system. UMD drive ditched and replaced by 4-8gb on board flash memory. Other upgrades: 2nd analog nub, touchscreen, blutooth, motion sensor. Design: Flip-style or slider. Size: Think Iphone. Cost: $199. Will be profitable on day 1.