The original PlayStation released on December 3, 1994 was the first of the ubiquitous PlayStation series of console and hand-held game devices. It has included successor consoles and upgrades including the Net Yaroze (a special black PlayStation with tools and instructions to program PlayStation games and applications), "PSone" (a smaller version of the original) and the PocketStation (a handheld which enhances PlayStation games and also acts as a memory card). It was part of the fifth generation of video game consoles competing against the Sega Saturn and the Nintendo 64. By December, 2003, the PlayStation and PSone had shipped a combined total of 102.49 million units, eventually becoming the first video game console to sell 120 million units.
PCSX-Reloaded is a PlayStation Emulator based on PCSX-df 1.9, with support for Windows, GNU/Linux and Mac OS X as well as many bugfixes and improvements. You can find official version on PCSX download page. You can also find some newer SVN builds at ConsoleEmu.
OpenEmu also emulates Playstation. You can find more info on OpenEmu homepage and download the latest version from here.
If You want to fiddle with building (compiling from source), Mednafen also emulates PS1 and is used as a core in OpenEmu. You can check it out at Mednafen homepage.