Are there any open source test automation tools application to regression testing for web applications?

You may also want to take a look at http://www.sikuli.org/. It's less widespread than Selenium but still is a good candidate.

Yes, Selenium2/Webdriver + a language at your choice would be the best option in my opinion. Also, together with a CI like jenkins, hudson, cruisecontrol you can have a very stable and helpful web testing framework. U might also use SaceLabs as they now have a fully-free version for open source companies.

There are several tools like Selenium, TestingWhiz, Watir, Regression Tester, etc. There are more details mentioned in this article - http://www.softwaretestinggenius.com/a-complete-guide-to-performing-automated-regression-testing

Though its not an open source one but you can get their free community version, I would suggest you give a try to TestingWhiz- http://www.testing-whiz.com/. Which is awesome in terms of its capabilities to test web, mobile and cloud apps for functional testing, database testing, mobile apps testing and web service testing, with features of ditributed test execution and its speed of regression testing.

There are many open sourced test automation tools available which can be used for regression testing of web applications.   Open Sourced Tools: Selenium, Robot Framework, Watir, MAX Q, Solex   But the most used and popular tool is Selenium for its multi browser & multi language support. http://www.qasource.com

For Web applications stick with selenium. If you want to scale and do parallel execution use selenium grid. Also you can try http://saucelabs.com . You can use selenium as a PAAS on sauce labs. Another option is http://borwserstack.com

Take a look at http://contizee.com . It is completely browser (plugin) based collaborative framework with which you can record/playback (generates javascript) and run in ready made client cloud. It has a pretty sophisticated point-click-customize javascript means (called checkpoint) by which you can generate test case validation logic directly while recording. It supports push button launches, CI integration, scheduled runs etc. And you can run selenium test cases too from the command line by making some small changes to  your Se code (call some APIs in their jar for connecting to client cloud and for reporting to the dashboard).