xdeb.org

The first Internet application I ever used was Fetch, a FTP-client for the Mac. This was in the early 1990s, before the web. The IT-staff at the University showed me how to use it for downloading shareware and freeware from Info-Mac and other places.

The first version of Fetch (Wikipedia link) was released 1989. When we are talking about Internet applications that is maybe not ancient but certainly very old.