Sony has stated that there are no plans to bring the PlayStation 3's Trophy system to the PSP, citing the security problems experienced by the handheld as one of the chief reasons.

While the hardware may have undergone a recent overhaul in the shape of the PSP go, Director of PlayStation Network Operations Eric Lempel told Joystiq at last week's E3 that Trophies won't be one of the features ushered in by the redesign. 'If people can artificially inflate their rankings and amounts of Trophies,' said Lempel, 'it kills the whole system.'

http://au.psp.ign.com/articles/992/992905p1.html

But cant trophies be hacked on ps3 x360 etc? Is that a good enough reason?

Well tbh its a portable machine, and trophies IMO arent tht important... achievment junkies already have a 360 or a PS3 anyways... tough it would have probably boosted some select PSP titles sales thats for sure :|

Yeah but trophies on PSP would enrich my experience...and I know I'm not the only one craving them....

it's to late in the PSP time, PSP2 however is another story.