Following are most important tools used for both functional and regression testing:
Quick Test Professional (QTP):HP Quick Test Professional is automated software designed to automate functional and regression test cases. It uses VbScript language for automation. It is a Data driven , Keyword based tool.
Rational Functional Tester (RFT):IBM's rational functional tester is a java tool used to automate the test cases of software applications. This is primarily used for automating regression test cases and it also integrates with Rational Test Manager.
Selenium:This is an open source tool used for automating web applications. Selenium can be used for browser based regression testing.