Are you wanting to play old games on the PS1/PS2? Or play PS1/PS2 games on the PC?
Zophar.net's List of Emulators for the PS1 (Arcade, GameBoy, NES, & Spectrum emulators)
Zophar.net's List of Emulators for the PS2 (Atari 5200, Commodore 64, NeoGeo CD, NES, BBC Micro, Sega Master System/GameGear, Spectrum, Genesis, SNES, & Turbografix-16/PC-Engine emulators)
The best emulator to play PS1 games on your PC is ePSXe, which can be found at
http://www.epsxe.com/. As for PS2 emulators for the PC, there are some, but most are in very early development and don't run any commercial games or maybe 1 or 2 games at best.