My web server, primary DNS, sendmail and mailagent are running on a 386DX/33 running Slackware. It's got 8MB of RAM and two 200MB hard drives. I've upgraded it to a 2.0.10 kernel (which I compiled on my Pentium/90 Debian machine -- much faster). Upgrading Slackware to a 2.0.x kernel was somewhat painful -- my next upgrade will probably involve switching the whole system to Debian. It also acts as a router, connecting my home LAN to the Internet full time over a 28.8k modem. I don't run X on it.
Cheers, - Jim