Open source test automation tools for functional testing of web applications

I would recommend Selenium, because of its superior handling of JavaScript. Specifically, I would recommend Selenium 2.0 (now available as an alpha version): it has been recently integrated with WebDriver to improve its API, and is consequently much easier to use.

Have you looked at Selenium?

It is widely used.

Another well known framework is Watir, using Ruby and its .NET counterpart Watin.

Watir - 'Web Application Testing in Ruby', a free open-source family of web automation libraries in Ruby. The libraries support IE on Windows, Firefox on Windows, Mac and Linux, Safari on Mac, Chrome on Windows and Flash testing with Firefox. Note: Firewatir (targeting Firefox) is now merged with Watir. For a listing of additional tools that are available to extend some capabilities - see the Watir site and also Alternative Tools for Web Testing' page at the OpenQA site for more info.

Here is some more info for the many other testing tools http://www.softwareqatest.com/qatweb1.html

Here is the comparison:

Another option is Sahi http://sahi.co.in/ It is well suited for applications using a lot of AJAX and Javsascript because it does not need any wait statements (automatically waits for AJAX and page loads), automatically locates elements across frames/iframes, has stable smart accessors which do not use XPaths, but rather uses relational APIs like near, in, under etc. It also has recorder/accessor spy for all browsers. It has drivers in Sahi Script (Javascript), Java, Ruby and PHP.