SAJAX (http://www.modernmethod.com/sajax/) is the Simple AJAX Toolkit, and has a server-side  implementation in PHP (among many other languages). Essentially, using this library, you can define  functions in PHP and call them from the client via XMLHTTP request. To enable a given function for  remote procedure call requires only one SAJAX function call: sajax_export(`phpFunctionName').

Unfortunately, SAJAX does not help when it comes to the necessary DOM manipulations. In fact, because SAJAX treats the response as text and inserts the response directly into the document using the innerHTML property of a given element (which is often considered inferior to DOM manipulations),  DOM manipulations are not possible unless you implement your own string parsing algorithm.

On the SAJAX frequently asked questions page (http://www.modernmethod.com/sajax/faq.phtml), the developers list "Not overly abstract" as a feature. Many aspects of XMLHTTP communication could benefit greatly from abstraction, so you might consider SAJAX's lack thereof as a drawback. Still, SAJAX offers a method of simplifying the server-side handling AJAX requests from the client and the client-side handling of instantiating XMLHTTP request objects and issuing necessary requests.

CPAINT

CPAINT (http://cpaint.sourceforge.net/) is the Cross-Platform Asynchronous Interface Toolkit.
It supports both plaint-text and XML response types. Additionally, it has some support for retrieving responses directly as JavaScript objects. The library is mature and actively developed.

CPAINT generates the XML for you from function calls, and the result is a somewhat non-semantic structure. Also, for some unknown reason, the generated XML elements are all in uppercase. If the name you supply for an element is not in full uppercase, the library converts it to full uppercase. The documentation of library usage is a little tough to get through, but each part of the puzzle is explained well and a trivial example is given for each to help you grasp the idea.

JPSPAN

The primary goal of JPSPAN (http://jpspan.sourceforge.net) is to bridge the gap between JavaScript and PHP. It allows for seamless importing of PHP classes to JavaScript. This means that you can define a class in PHP and call its methods as if it were a native JavaScript object. Behind the scenes, JPSPAN is issuing requests to the server to execute methods remotely. Other libraries offer similar functionality, but they do not come close to the abstraction offered by JPSPAN. Documentation and example code for JPSPAN are abundant and clear. Both are in wiki format and are thus ever-growing. The code itself is clean and easy to read, just like the XML it generates. Furthermore, initial work is currently under development to embed JPSPAN in PHP frameworks to make it even easier to develop fat-client applications.

The library does not offer relief from DOM manipulation tasks, but it does abstract the usage of XML-HTTP quite well. Unfortunately, it seems to have problems supporting Opera, but it supports Mozilla-based browsers and Microsoft's IE quite well. Additionally, depending on your application, a bridge between JavaScript and PHP might not do you a lot of good, and only serve to exchange XML tree traversal with object and native JavaScript accesses.

As there is additional overhead involved in creating the native JavaScript versions of PHP classes, the benefits might not outweigh the costs. However, because of the excellent use of abstraction, JPSPAN could allow you to almost completely ignore the details of how PHP classes are being made available to JavaScript and focus attention on the functionality of the application itself.

There are many other AJAX libraries that support PHP. You can learn more about various AJAX libraries at http://www.ajaxpatterns.org/AJAXFrameworks.