The PSP's got a number of really neat titles.
I tend to gravitate away from general "shoot stuff" kinda games. Not because I don't love shooting stuff, but because there are so many games on the PSP that bring something more than just "shoot stuff" to the table.
If you haven't already, look into Patapon and Patapon 2. Music oriented, strategy based, wonderfully delivered.
Crush is another great one for that. Greatly delivered puzzle game, with an awesome soundtrack.
Puzzle Quest is also great. I think they recently did a Puzzle Quest in space.
If you like RPGs, Valkyrie Profile is pretty good. So is Star Ocean. If you like the turn based kind, Jeanne D'arc was very good. Historical setting in that one too. Umm... Final Fantasy Tactics is a staple. Disgaea is also a very very very very awesome game.
Other general do-not-miss-these games, in no particular order; Daxter, Crisis Core, Metal Gear Portable Ops, Wipeout Pure, Burnout Legends, Tekken, and... hmm... Oh! Hah, Lumines. It will be very hard to find, and if you walk into a store asking for it, the person there might think you're trying a very very old way to hack your PSP. But the game itself is very good.