There's no shortage of emulators for older gaming consoles on modern mobile platforms. The latest addition to the list is PPSSPP, a PSP emulator that self-admits to being a work in progress. Of course, there are a couple of things you should know up front: for starters, it's possible this won't last long on the Play Store, since emulators tend to have a pesky problem with legal and policy gray areas. Secondly, the app is still in early development, so many games will likely not work. You should expect a level of beta-ness on this one. Heck, it's only listed as version 0.2.
As always, this is a bring-your-own-rom situation if you want to play any games, and there's no guarantee that any of the ones you get will work. Still, it may be fun to try out. If you want to help improve the emulator or work on the project, you can read more about it here.