Promoting itself as "the easiest way to develop asynchronous Ajax applications with PHP", xajax over on SourceForge seems to fit the bill.

xajax is an open source PHP class library that allows you to easily create powerful, web-based, Ajax applications using HTML, CSS, JavaScript, and PHP. Applications developed with xajax can asynchronously call server-side PHP functions and update content without reloading the page.

They list a few reasons to use their library over the other out there too:

• xajax's unique XML response / javascript message-pump system
• xajax is object oriented
• xajax works in Firefox, Mozilla, probably other Mozilla based browsers, Internet Explorer, and Safari.
• xajax can be used to update styles, css classes, checkbox and radio button selection, or nearly any other element attribute.
• Using xajax you can dynamically send additional javascript

And much, much more...If you've been looking for a quick way to get up and running with an Ajax application on your site, you might want to give xajax a try to see if it suits your needs...