The PSP has games? The best thing you can do with your PSP is hack it, but I can't talk about that here. :\
Well, there are a few good games on there. If you are into racers, Wipeout Pure and Ridge Racer are safe choices (and if you're getting Wipeout, scrounge up the European version -- it has more downloadable content). If you are into fighting games at all get Tekken on the PSP, it's a really good port of a solid iteration of the series with a lot of added content. Lumines and the sequal (called Lumines 2, natch) are good puzzlers -- 2 has more content, but 1 is insanely cheap now.
For more estoric choices, I would go with Every Extend Extra (crazy shooter/puzzle game hybrid,
the origianl version is avaialbe free on the Internet), Exit (puzzle/platformer game kind of like the old Prince of Persia games), DJ Max P (Korean music-rhythm game), and IQ Remix (a puzzle game that I really can't describe in a sentence).
Too bad 90% of the library is just bad ports of PS2 games. :\