The WWW Virtual Library

This is one of the oldest, if not the oldest site, still up on the Web.

The footer of the site say it was last updated on Tuesday, February 21, 2017 - 0:02:41 GMT.

Pulled from the website itself:

"The WWW Virtual Library (VL) is the oldest catalogue of the Web.

It was started by Tim Berners-Lee, the creator of HTML and of the Web itself, in 1991 at CERN in Geneva."