No, you may not play PSP games, however! You can play:
NES, SNES, GBA, GB, GBC, Genesis, SMS, NeoGeo, and a few other 'older' console games.
I'm sorry that a lot of people decided to basically flame you for asking this question, and you should know that most of the people here are nowhere near as bad.
The reason why you cannot emulate the PSP and why the R4 cannot play it, is because the DS is a little weaker in computer power than the PSP is, and even then they use different hardware entirely, so it'll most likely never happen, although ways have been suggested, the chances are near nil.