Ones I have personally used and endorse (will play most games at full speed with sufficient hardware) will be marked by an * (asterisk). For more emulators and systems go to: my main thread
==========================================================================
*ePSXe: Great compatibility, it is probably the most updated of the high-compatibility PSX emulators.
*PSXeven: a good runner-up to ePSXe, but no longer maintained. It USED to have better compatibility with a number of RPGs than ePSXe, but this is no longer true with the newer versions of ePSXe. It is also somewhat less stable than ePSXe.
-PCSX: a decent PSX emulator, made by the team that later created PCSX2. It is no longer maintained (they quit updating it to work on the PS2 emulator) but has had a couple of forks that were continued.
-PCSX-Reloaded: a fork of the older PCSX emulator, it is more current, with the 1.9.92 beta being released in 2010.
-pSX: a fairly compatible emulator whose last update was around 2007.
-AndriPSX: this emulator has been updated on and off since 1999. although it does not have as high as compatibility as most other emulators, it is a good choice if you are running on older hardware.
-SSSPSX: a Japaneese emulator for the PSX, it is moderately current, the last news I could find was from 2012, listing it as beta status, but the domain listed as its home website has been unregistered for a while.
-Bleem!: a free, then commercial, then free again emulator, it was one of the first PSX emulators for Windows (and the DreamCast) and was sued by Sony when it was commercial software. While Sony did lose the case, Bleem! was forced to shutdown for monetary reason (from the legal fees incurred). It used many various tricks and hacks to get games running on the then-current hardware, and so it is quite buggy. Not recommended unless you want to check it out for historical reasons, as 'The Emulator Zone' alleges to be the first commercial emulator, and it was the most memorable commercial program to emulate a current console.