Sony PlayStation Network boss Eric Lempel has stated "you're not going to see Trophies on the PSP".
He told Joystiq during E3 that there are "a few reasons" for this. But the biggest is security of the platform, as people "artificially inflating their rankings... kills the whole Trophy system". The PSP has a history of home-brewed software, a scene that Sony has tried to stamp out with frequent firmware updates.
I guess due to the home-brew PSP scene they feel like they can't rely on their trophy system being safe from hackers. Maybe we'll see trophy integration with the PSP 2 someday. I personally would like to see trophy integration with some 3rd party PC games also since Xbox gamers get achievements from some PC games.