PPSSPP Gold is the best, original and only PSP emulator for Android. It runs a lot of games, but depending on the power of your device all may not run at full speed.
Play PSP games on your Android device, at high definition with extra features!
No games are included with this download. Dump your own real PSP games and turn them into .ISO or .CSO files, or simply play free homebrew games, which are available online. Put those in /PSP/GAME on your SD card / USB storage.
See http://www.ppsspp.org for more information.