Sure. IIRC, every Mac comes with a copy of Apache (and if not you can download it for free). Here's an article about getting it set up (it's for OSX 10.2, so it's a bit dated but it should all still apply to 10.4):
Then you won't be able to use a registered domain name, as that would require a static IP for the Domain Name Servers to use. Unless, of course, someone more knowledgeable than me can come up with a solution. 🙂
Edit: FWIW, ASO will host you for $25/year. Pretty decent if your bandwidth requirements are low.