Here is an interesting article on JSON (http://www.informit.com/guides/content.asp?g=xml&seqNum=268). It has some great examples of what JSON really is and how it works.
Before we go any further though, we should spend some time discussing what exactly AJAX and JSON are.
That is AJAX in a nutshell. I personally like to use the prototype.js library myself, though there are others out there and most of the big name companies are integrating AJAX support into their products.
JSON is positioned to compete with protocols like SOAP which was designed to allow applicaitons to communicate easily. In the example article above, the author takes advantage of the src property of script tags to fool the browser into making a request (similar to AJAX but using a different method). I imagine you could use this same technique with AJAX to make requests to the remote server. The down side to this is that all requests are made via a GET request where AJAX can support GET or POST requests.
JSON is not positioned to take the place of AJAX, they are really different animals, but I can see the potential of utilizing the two together. Rather than have to resort in trickery to get your JSON information from a remote site, have your AJAX request return JSON information and send it to the JSON parser. This could potentially save you some coding when trying to parse the XML information returned via teh AJAX request.
Correction: During further review of the prototype AJAX library, I noticed that it posseses JSON capabilities already. Something to keep in mind anyway.
All in all, some very good examples, go read the article!
Computer Magic And Software Design