The campaign website for Dole/Kemp '96 is still available on the web. The entire front page at its actual size fits in this image...man, screens used to be tiny.
The Clinton/Gore '96 site no longer seems to be available (cg96.org is a parked domain, covered with ads), but 4president.us has some archived screenshots and a press release of some remarks by Al Gore on the site's launch. We've come a long way since then.
This is the first thing you see when you go to our home page, and it has a couple of innovative features for those of you who are familiar with the Internet and the World Wide Web. It's not very common to have this kind of ticker with a changing message at the bottom constantly moving or to have a server pushing new pictures onto the page with regularity right to your own computer.
Anyway, this is the first thing that you see, and then we go to the main menu. Since 1992, Bill Clinton has been working tirelessly to insure that America forges ahead and leads the world in the information age. He has brought technology into our classrooms and libraries, he signed the historic telecommunications reform bill to make sure that all of our cabinet agencies are online. Together, not long after we got into the White House, we became the very first President and Vice-President to have e-mail addresses and to set up a White House Website. I hope all of you have had the opportunity to visit the White House Website.
4president.us also has screenshots from other campaign sites that year, including those of Steve Forbes and Pat Buchanan. (via @kdawson)