A new emulator is currently being developed by the fine folk who brought the world the fully working Wii emulator called Dolphin for PCs. Apparently the developers got a hold of an Android device finally and decided to do what they do best, build an emulator. However, this particular emulator isn't another GameBoy or console emulator, which we have plenty of. Instead, this emulator, called PPSSPP, is a Playstation Portable emulator for Android.
As of right now, PPSSPP is a fully working Playstation Portable emulator that will let you play PSP games on your Android device. Even though this is a fully working PSP emulator, development is still considered to be in the early stages so there might be a few bugs that you will have to deal with. However, it is already able to play certain games at full speed and it does have a pretty slick UI for you to use to navigate through things.
Feature-wise, there are currently only a few features available since it is still early in its development and PPSSPP is missing a few things such as no mapping of hardware keys right now and normal legal PSP eboot files are unsupported. PSP ISO files do currently work though. Interestingly enough, the way the developers made this allows it to run on most Android devices, not just high-end ones, as long as your device supports OpenGL ES 2.0. Of course it is a definite plus having it on a higher-end Android device.
If you want to give PPSSPP a whirl, you can do so for free by downloading it off of the official PPSSPP website. It is 100% free and open source as well. Just keep in mind that development is still early so game compatibility is limited right now although that will change pretty fast.