Ajax: A New Approach to Web Applications by Jesse James Garrett

Ajax isn’t a technology. It’s really several technologies, each flourishing in its own right, coming together in powerful new ways. Ajax incorporates:

• standards-based presentation using XHTML and CSS;
• dynamic display and interaction using the Document Object Model;
• data interchange and manipulation using XML and XSLT;
• asynchronous data retrieval using XMLHttpRequest;
• and JavaScript binding everything together.

[...] The biggest challenges in creating Ajax applications are not technical. The core Ajax technologies are mature, stable, and well understood. Instead, the challenges are for the designers of these applications: to forget what we think we know about the limitations of the Web, and begin to imagine a wider, richer range of possibilities.

Some examples of Ajax:
Google Maps, BXE, Flickr. map.search.ch uses Javascript, but I am not sure if it would qualify as AJAX?

UPDATE:
Dare Obsanjo doesn't like the newly coined term Ajax. Here he says why.