What linux OS should I put on my old desktop?

If you got another 256M of ram, you could run Ubuntu quite well on that.

Without RAM, I'd personally go with TinyMe. Should run quite snappy on that.

Depends if you have had any prior experience, I assume you haven't. If so I suggest Ubuntu (www.ubuntu.com) since it is the easiest and most intuitive linux distro ever made. If you want to kick it up a notch in difficulty go for Fedora or Debian. Or if you want something harder to use go for Arch. I've tried them all, Arch is really good since it's really small, but ubuntu is probably the best choice.

Puppy Linux.

I thoroughly recommend Linux Mint 9 FLUXBOX which is ideally suited to older hardware. Its easy to install and easy to use plus it comes with much of the software you are likely to need preinstalled

Linux Mint 9 FLUXBOX Download

http://www.linuxmint.com/edition.php?id=65

Linux Mint 9 FLUXBOX Release Notes/User Guide

http://linuxmint.com/rel_isadora_fluxbox.php

You download the ISO. image of Linux Mint 9 FLUXBOX then you need to create a Bootable LiveCD for installation

Linux Mint 9 FLUXBOX can also be run direct from the LiveCD from Booting up without touching your Hard Drive

LUg.

Get xubuntu at http://www.xubuntu.org/

Its just like ubuntu except its made for less capable (older) hardware