Here is a list of top free PSP or NDS emulators for android, which you can download from the Play store. Put all that power which your Galaxy S3, S4 or HTC One has to good use. To check compatibility of specific games such as God of War PSP Games (my favorite), visit the Compatibility forums link below. http://forums.ppsspp.org/forumdisplay.php?fid=5
PPSSPP is a PSP emulator for Android and other platforms. It runs a lot of games, but depending on the power of your device all may not run at full speed. See http://www.ppsspp.org for more information.
nds4droid is a free Nintendo DS emulator. It is still in it’s infancy but supports many features you’d expect like save states and sound. It also supports the OUYA game console.