AJAX came about as a result of web developers looking to provide a better user experience.
Previously to AJAX, developers would invariably have to refresh a page in the traditional way in order to deliver new or amended content.
The use of live page updates allows users to receive a far more seamless experience and there are now countless examples of this around the modern web today.
JSON and XML are formats of data which require thorough validation as any errors will likely impact a website far more than, say, a missing close tag in a standard HTML5 or XHTML page. Various validation tools can ensure that your data is constructed correctly and can be built into the development and testing stages.
These technologies tend to be used in all of my contracts, and are very much a part of the standard Front-End developer’s makeup these days.