Depending on how much functionality you want there are plenty of distros. I have a pentium 90, running a mysql server, php, apache and some mail server stuff. The hardrive is only 840MB and it runs like a champ.

The distro is Debian. Debian can be a very large system (like redhat) if you chose to install all the packages, but if you just install the base system, its about like Slackware (one of the smallest distros), with a nice packaging system. Again when you install the base system just make sure that you install only what is needed.
Hope this helps!