One Man's Dream: Walt Disney World
One Man's Opinion: Rain at WDW is over-rated.
I spent years "worrying" about rain and charting weather before going. I always thought we'd been lucky. Then I found out we'd seen it at its worst. Unless you're unfortunate enough to get hit by a hurricane, it just isn't that bad.
We find that while there in September (the worst rain I've seen), there is usually a mid-afternoon burst lasting 30 to 45 minutes. It lowers the temperature, and if you have proper raingear (good advice above), you can use it to your advantage. We find whatever ride we're in when it starts, if we're willing to walk in the rain (or sing in the rain!), we've got walkon at the next ride. Note that a few rides (Test Track comes to mind) will not operate in the rain.
We also found an early evening shower most days. Same affect. We had ponchos. I think my shorts got wet. I enjoyed the cooling affect, and inside fifteen minutes after storm, my shorts were dry and I was whining about the heat.
So take all the advice here, and just don't worry about it!
The biggest plus of rain at WDW: There's nothing like a rainbow over Epcot (except maybe a rainbow over MK, AK, or MGM). So when it does rain, don't forget to look for the rainbows!
Pat