Crisis Core Final Fantasy VII
Tekken Dark
Jeanne D'Arc
Metal Gear Solid Portable Ops
Final Fantasy Tactics

For God of War, just wait 'til the price drops to $20. The game is short, and there's little stuff to do after you beat it.

- Holy Mother of freaking Yahweh! Monster Hunter Portable.

All these games are quite good. I also recomend Metal Slug anthology if you havn't played metal slug heavily before or if you are a huge fan.

OOORRRR, Instead of asking us of our opinions,  you might want to check out Game Rankings Top 10 or Top 20 games on the PSP. 

With that said, on the PSP there are really two types:  The games that are quick fixes,( really easy to play or don't take up hours of your time) or the ones that are more like the standard releases for the PS2. ( longer games)

My Personal Top 3 of each type:

A.  Quick Fixes= 1. Patapon, 2. EchoChrome, 3. Loco Roco

B.  Standard Games= 1. God of War: C.O.O. , 2. Final Fantasy Tatics ( don't worry about the story on this one, it's an update of a previous version) 3. Metal Gear Solid: Portable Ops

patapon and ape escape on the loose psp store download

don't ever get star wars battlefront rogue squadron it took me 2 hours and 20 minutes to beat the game.

But it was a game built for the multiplayer ... and that rocks for a handheld game ;)