Eh to be honest, I think both of the current portables have failed to live up to the standards of both companies.
To, for all intents and purposes, unlock the PSP's "full potential" if you will, you're going to have to get custom firmware (as in emulators). I'm assuming you bought a PSP-3000? Because at the moment you can't get CFW on that version of the PSP. As much as I **** to say it, the PSP has absolutely nothing going for it right now; it has massive potential as seen from games like God of War: Chains of Olympus, but Sony hasn't scored too many big games since then.
As for some good games:
God of War: Chains of Olympus
Megaman Maverick Hunter X
Megaman Powered Up
Star Wars: The ***** Unleashed
Twisted Metal
Lego Star Wars 2
Lego Indiana Jones
Lego Batman
Marvel: Ultimate Alliance
Mortal Kombat: Unchained
Dragonball Z: Shin Budokai - Another Road
Metal Gear Solid: Portable Ops or Portable Ops Plus
Metal Gear Acid 1 and 2
Chili Con Carnage
Ratchet & Clank: Size Matters
Daxter
Grand Theft Auto: Liberty City Stories or Vice City Stories
Crisis Core: FFVII
the Capcom Classics Collections
Castlevania: The Dracula X Chronicles - this is pretty good, as you get two or 3 other big Castlevania games you can unlock too
Killzone: Liberation
That's pretty much all the big name PSP games.