Ever heard of PPSSPP?
It's a fast and portable PSP Emulator, written in C++, and works on Android!
You must be kidding, author! My PC even can't run PSP emulator!
That's why, don't be so excited, it's still in early stage, and there are not so many compatible games, actually only one fully compatible game works for now, but you can see the potential here. At first we were given the GBA emulator, also don't forget the FPSE - PS1 Emulator- too. See? This thing is getting crazier now :)
So, you still don't believe?
Here, you can access this site
You can also download the APK from the developer site, or click here, i've made it easier for you :D
Don't ask for the compatible games, as i've stated before, the only game that is working now is&Puzzle Bobble Deluxe.
Last words, keep the good works developer!