Package ID: org.ppsspp.ppsspp
PPSSPP is the best, original and only PSP emulator for Android. Not all games run perfectly yet but it runs a lot of games. No games are included with this download, see below.

Some examples of compatible games (not all will run full speed on all devices):
Persona 2, Persona 3
Little Big Planet
Burnout Legends, Burnout Dominator
Final Fantasy : Crisis Core
Monster Hunter 2 Unite
Soul Calibur
GTA (slow on mobile)
Daxter
Lumines
Worms
and many more...

Operating System: Android Froyo (2.2)+