Playstation
What Nintendo did with the NES, Sony did with the Playstation to the extreme. Currently one out of every four households in America has a Playstation. It is THE most succesful game system of all time. It was also the first system to have outright copy protection on its games, which in turn lead to a whole new industry, the modchip/game enhancer industry, but that's another story for another time. We're here about emulation.

The first emulator you don't go out and get is bleem! It had it's chance, and it failed. Lousy customer support, infrequent updates, and it just didn't work that well. It is now dead and buried. Leave it there.

Next we have Virtual Game Station from Connectix. Oh, wait. Sony bought Connectix, and so there won't be any further updates for this product, either. However, if you do have it, it's not a bad program. It's very easy to set up and has a high compatibility rate. If you happen to be running Windows 2000/XP, don't worry. Sapu released a patch for it here.

Finally, we have ePSXe, which stands for Enhanced Playstation Emulator. That's right, this nifty little program not only lets you play PSX games on your computer, it makes them look better, too.
Rather than give a whole tutorial here, I'm gonna point you to an excellent one already written up. Head on over to Easy EMU and click on the ePSXe tutorial in the left frame. Please take the time to set it up, it really is worth it.

Gradius Gaiden Strider 2 Pepsiman

LINKS

Official ePSXe Website
Emulator Homepage

Sapu's Website
Virtual Game Station XP Patch

Aldo's Tools
Lots of neat PSX emulation stuff

Easy EMU
Excellent site for the emulation newbie