

Current Version: 1.3 (as of September 17, 2016)
http://www.ppsspp.org/
PPSSPP is an up and coming PSP emulator that has been created from the ground up using C++ (where as JPCSP uses Java). This means it can run on a much larger variety of specs smoothly even with a lower end PC. No BIOS needed. (For a point of reference, I have a laptop 2.1ghz dual core, ATI Radeon Mobility 4250 HD, 3gb RAM, and it runs pretty smooth with some random slow downs. Believe me, you can run it well).
There are dedicated developers behind it constantly pumping out updates and fixes for it. They've even managed to develop their own atrac+ decoder which is required for a lot of sounds, especially in cutscenes.
Works even on mobile devices, namely Androids. There are also builds for iOS, Blackberry 10, Mac, Linux and more, but these are more complicated to install.
http://www.ppsspp.org/downloads.html
PPSSPP Gold for Windows via Paypal (a donation essentially)
Google Play Store:
PPSSPP Free
PPSSPP Gold if you want to support the developer
Known game compatibility list:
http://forums.ppsspp.org/showthread.php?tid=1473
Frequently updated builds:
http://buildbot.orphis.net/ppsspp/
Some images from Seik (hope you don't mind I'm stealing your pics lol)
Going to link to the images so you all don't have to reload massive pictures.
Metal Gear Solid Peace Walker
Crisis Core: Final Fantasy 7
Even more Crisis Core
Kingdom Hearts
Thanks to ambientmystic, Stuart444, and Seik for their contributions to my uncreative OT.
Let me know if I forgot anything.
Tips and Tricks from our favourite AmbientMystic:
Just a minor heads up.
I've updated my generic performance guide for PPSSPP (for Windows and Android) here:-
http://forums.ppsspp.org/showthread.php?tid=5236
Also wrote up an easy to follow guide for compiling PPSSPP on Windows in case any gaffer is interested in self-compiling PPSSPP (independence from the buildbot is a great thing) on their systems:-
http://forums.ppsspp.org/showthread.php?tid=5231