RPCS3 is an experimental, open-source PlayStation 3 (PS3) emulator. Currently usable for small homebrews and a decent number (about 50%) of commercial games, it aims to eventually emulate the PS3 fully.
RPCS3 now works for many commercial games at playable speeds (even supporting high-resolution rendering!), but emulation is not quite perfect and can be still slow and buggy. Notable games that works (at full speed provided you have good hardware) include Demon Souls, the Project Diva series, Catherine and more. Some other games will either not work, be too slow, too buggy, or only gets an intro. Wait a while longer if you want good compatibility/few glitches/fast emulation.
A compatibility list can be found here.