Wipeout Pure was fantastic, be sure to get all the DLC if you can find it. If you've never played a God of War game before, get God of War: Chains of Olympus. For a puzzle game, I'd suggest Crush. Severely underrated IMHO. Daxter was a decent platformer (I'd wager it's the best on PSP), but was let down by some maddeningly difficult minigames.
Coded Arms: Contagion Field Commander Grand Theft Auto Liberty City Stories Killzone Liberation Syphon Filter Dark Mirror Syphon Filter Logan's Shadow WH40K Squad Command Wipeout Pure (as Beasteh said) Wipeout Pulse
Medievil Death Jr Medievil has extra mini games in it on PSP compared to original, other than that though it is the same game as the original PS1 game. Death Jr is a great 3D platformer.
Needless to say, if you're into your jRPGs, final fantasy 7 through 9 are absolute must-haves. I bought my psp 3000 purely for ffvii in my pocket. There's also a highly rated psp remaster of silver star harmony too, although I found it to be a hugely overrated game. More nostalgia goggles than anything else going on there I think.
If your into racing games at all go for Gran Turismo, its pretty good on the psp however there is no career mode so does eventually get boring
