Not everyone knows that the CloudBees build servers come with browsers on them - so you can do "headless" browser GUI testing.
However, it really depends on the testing framework you are using - my recent experience with Angular.js showed how easy it could be with the testacular framework:
In the above testacular.conf.js config the browsers to run the tests in are listed - and it Just Works (I was surprised !). You can also have Jenkins publish test results as HTMl from the test report generated.
If you are interested in looking further - check out the angular.js clickstart - and take a look at the project structure, and the build script it sets up for you in Jenkins.