Editor's Note: This entry deals mainly with the older Mac OS, not Mac OS X. For details on running OS X on x86, see this entry: »All things Macintosh »Can I run OS X on my non-Apple PC?
I have complied a list of URLs and will explain what you need to get started.
First off, there are basically two major (only?) Mac emulators. Neither will emulate a PowerPC chip (but check the second update, below). Both do 68k emulation. They are Basilisk II (originally a BeOS app, iirc) and SoftMac. Both emulators also require a Mac ROM. These can be "legally" copied from a 68k Mac that you own. Or the other option is to buy this 150 dollar card. I'm not gonna explain any other ways to get the ROM. This a list of all the Mac ROMs that may or may not work.
After you have acquired a ROM file, you will need an OS. These emulators only support 7.5-8.1 because they are 68k emulators. 7.5.3 is available for free download on Apple.com here. That's great and all, but most software you will want to run will require 8.1 or even 8.5+, which would mean that you are out of luck. If you can get by with 8.1, you may have luck finding a cheap copy on eBay, OWC, Smalldog, or you can order it from the SoftMac store here. It comes with ClarisWorks, 8.1 and a few others. But the price is incredible, 199 bucks for almost a decade old software.
If you are still up to the challange and feel it will be worth while, check out these sites:
SoftMac Documentation -- Helps you get the whole thing started
Benchmarks and Requirements for SoftMac -- what level of performance you can expect
SoftMac Screenshots 1 | SoftMac Screenshots 2
Basilisk II for Windows
General Mac Emulation Set up guide
Coma points out that there are a couple more: the Spectre GCR and the Gemulator 2000
steven s points out that PearPC emulates a PPC on x86 machines and so can run OS X, though only very slowly at this time (5/04).