PPSSPP can run your PSP games on your PC in full HD resolution, and play them on Android too. It can even upscale textures that would otherwise be too blurry as they were made for the small screen of the original PSP.

Here's changelog for 0.9.6(-2) release:
+ Large general speed improvements and assorted bug fixes
+ "Software Skinning" option which speeds up many games with animated 3D characters (but may slow down a few, like Monster Hunter - experiment with turning it off)
+ Various fixes around stencil/alpha, reducing glow problems in Wipeout and Gods Eater Burst.
+ Timing improvements making more games run at the correct FPS, also fixing some audio issues
+ More debugger features
+ Better looking and individually resizable touch controls
+ Automatic install of games from ZIP files, like demos and many homebrew.
+ Software renderer improvements
+ VERY basic ad-hoc online play support, to be improved in future versions.
+ fixed bug that causes the game list on Android to either display a blank or crash if it sees a ZIP or RAR file

Visit Official homepage for for further information and latest build of emulator