19-year-old Mac doing server duty with NetBSD ... plus even older Macs serving up Web pages
A Macintosh IIci -- with 25 MHz of CPU power -- equipped with NetBSD is currently serving up Web pages and somehow surviving.
If you want to turn your ancient Mac into a server, start here (to use Mac software and find out about other ancient Mac servers), or here (to use NetBSD).
And if a IIci is too new for you, here's an Apple ][e (circa 1984) Web server, and a Mac SE. And here's an Apple Lisa server. (Thanks to The Old Apple Web Server Directory).
I looked for a similar homage to old PCs as servers, but all I could find were endless reiterations of the old "Hey, if you have an old PC, why not turn it into a web/print/file server?" I didn't see any "Here's my 386SX-25 or 486-66 that serves up Web pages."