This thread is for compiling really old sites from around the web. (Note: does not include popular sites that were founded in the 90s, so Google doesn't count)
http://www.spelljammer.org/ 1995 dnd site.
http://freefall.purrsia.com/ Webcomic started in 1997, still ongoing. 3198 comic strips.
http://cerulean.st/absurdnotions/ Webcomic started in 1989, ended in 2007, now back after 11 years! Possibly oldest webcomic.
milk.com Website established in 1994, owner refused to sell domain.
And http://musefanpage.com/blog/, a forum for a children's science magazine. Now the forum is mostly abandoned, but some of the now grown up scientists post about their work their.