We went last year, May 31st to June 14th. It pretty much rained every day. Apparently last year was a very wet year, so this was out of the norm, and the rain did last longer than usual.
We still had plenty of hot sunny weather, and most of the time the rain cleared within an hour or so. One thing I would advise is to get out early, as the sun always seemed to be out from around 8am - 2pm, then the rain would come.
We only had a couple of days that were complete wash outs, unfortunatey we were at Sea World and Epcot on those days!
Anyway we are going back June 11th, so didn't put us off!
Dave.