We went to WDW the last full week of 2002. It rained everyday except for the last. There was a hurricaine out in the gulf that sent in bands of rain everyday. The rain last anywhere from 10-15 minutes to half the day.
You can still go and have lots of fun at WDW in the rain. Just go knowing that it's going to be hot, humid, and rainy. These things can be dealt with.
Buy 2/$1 rain ponchos from Dollar Tree before you go. Buy lots of them. Carry them in your backpack. Also carry a gallon sized ziploc bag for each poncho. This way, if it only rains for 15 minutes, clears and then rains 3 hours later, you still have the poncho ready to use.
Carry a waterbottle and drink even when you don't feel thirsty. Dehydration is a bummer. The heat and humidity make drinking a MUST.
Scotchgard your backpack, sneakers, and fannypack. This will help to protect them and let you keep moving.
Carry a clean dry shirt and a couple of dry pairs of socks for each member of your party in a ziploc bag also. Sweaty or rainy soaked clothes are a joy killer.
We had a great time even with all the rain. It was our best vacation ever. It's important to remember that rain will not end your enjoyment of Disney. There is much that can still be done.
Maggie