GWT's advantages are well enumerated in a Slashdot comment:
* You get to use the same form verification logic on the client and on the server, which means you don't have to implement it twice, which makes it much harder to get it wrong.
* You completely avoid the horrific browser inconsistencies.
* You get a real debugger.
* For most tasks, the pain of connecting your front end to your back end is done for you.
Google also uses the framework internally, for services like Google Base, Image Labeler and more. Google says GWT is much more successful than they expected to be, and that's one of the reasons why Google decided to open source it.