I've had two hurricane related Disney World trips. Floyd and Frances. With Floyd, we were flying in and the airline (Northwest) easily and without penalty moved our reservations one day forward going and one day forward coming back. There were absolutly no problems at all. Disney easily extended our stay by one day as well. We were meeting my father and stepmother, the reservation was in my name but they would be there a full day before us. Not a problem.
For Frances, we actually were stupid enough to drive into the hurricane and were in a lockdown for 24 hours. When we arrived, the hurricane was far behind us. There were many, many people hoping to stay since their flights had been cancelled. Disney World made sure everyone had accommodations.
I think this has always been the Disney unofficial policy but now it's official. One of the reasons we went during Frances was because I knew if it did go through (and boy, did it!), we'd still be safe. When my family lived in the Keys for a decade, they would evacuate to Disney World because they knew they'd be taken care of.
And with both of these instances, if the entire Disney World parks are closed down, the one day was refunded. But if one park is open and you can get there, it won't be. With Frances (we arrived later for Floyd), the entire Disney World area was back to normal within 24 hours.
As with everything else, Disney World does hurricanes right.