I don’t think non-programmers will know the difference, I think you should provide some specific sites. Gmail, for example, has links at the bottom “basic HTML” gives you the non-Ajax version.

A couple of things I do like about Ajax sites:
Drag & dropping email into folders in Yahoo mail
Keyboard shortcuts “F = forward, N = New email message”

Your question did make me curious, so I reverted to the old basic HTML Gmail. I think the Ajax version initially loads slower, but then everything speeds up because it’s loading lots of stuff in the background.

Well there are right and wrong ways to use Ajax. I’ve visited a lot of sites that use it but have to wait on the response in order to continue—this really slows the experience down. On the other hand, sites like Facebook use it and still provide the ability to move forwards and backwards in the browser (for the most part) while doing the heavy lifting in the background.

And as @jaytkay mentioned, the Ajax version of Gmail seems to work perfectly fine on my end—the experience surpasses the plain HTML version IMO. This leads me to wonder if it’s a problem with your setup. Which OS and browser are you using? IE’s javascript engine is notoriously clunky and can lead to sub-par Ajax performance. I use Firefox and it works great—though I believe the fastest out there is probably Chrome.