PPSSPP is a PSP (PlayStation Portable) emulator capable of running the majority of the games made for Sony's first portable console right on your Android device.
The first thing you'll notice when you run PPSSPP (developed by one of the authors of Dolphin, the most powerful Gamecube and Wii emulator out there) for the first time is the large number of setting options. You can activate Vsync, anisotropic filtering and texture scaling, among others.
Controlling games with PPSSPP is much easier than it may seem at first. Smartphones with smaller screens could run into some trouble, but if you upgrade to a bigger screen, like a tablet, you'll find that you can easily master the controls.
The list of games that are compatible with PPSSPP is also impressive: Disgaea, Patapon, Soul Calibur, Little Big Planet, Final Fantasy VII: Crisis Core, Monster Hunter Freedom Unite, and GTA: Vice City Stories are just a few examples that you can play on your Android using this emulator.
PPSSPP is an excellent way to enjoy a good chunk of the PSP catalog using your Android device. Best of all, not only can you comfortably play all the games mentioned, but you can play them with better graphic quality than in their original versions.