Smashing Magazine lists a couple of free and commercial tools to cover cross-browser testing:
Good news: very powerful free testing tools are available for Web designers today. Some are more user-friendly than others, and some have significantly better user interfaces. Don’t expect much (if any) support with these tools. But if you’d rather not spend extra money on testing, some great options are here as well.
By the way, our own tool Xceptance LoadTest (XLT) offers a way to run cross-browser functional tests. XLT leverages WebDriver, a multi-browser API for automation. WebDriver does not support all browser and does not equally support all browser well, but we tried to iron out as much as possible. On top of it, you can use the XLT Script Developer to easily create automation scripts and run them either using our own scripting language or export them to Java to directly run them on the WebDriver-API.
You can download Xceptance LoadTest for free with no strings attached from our web site: www.xceptance-loadtest.com.