Hyperweb was, and is, an "an experimental hypertext site using HTML" — from 1996. The experiment itself, an interactive essay of sorts, starts here; you can click around, or watch it cycle through by itself.
The Froggy Page was the Cool Site of the Day from August 8, 1994. It's the oldest site archived there without the disclaimer, "site no longer live". The page sure looks like it was built in '94 -- not even a single table! (Can anyone who was coding back then confirm if the code is really that old?) Does anyone have a favorite site from those good old days?