We were at Disney in May of 2009 and had hours upon hours of rain each of the 7 days we were there. We weren't expecting that (forecast changed dramatically while we were there) but fortunately I'm an over-packer and we were prepared.
Here are the things that helped us the most:
1. I always make sure each person in the family has at least 2 pair of shoes. Most of us wear sneakers/running shoes so 2 pair of shoes was critical on this trip. Every evening I'd stuff the wet shoes with towels or washcloths to soak up the water. They'd be 90% dry by morning. In the morning I'd pull out the towels and let them air dry the rest of the way. They'd be good to go by the next morning.
2. Plenty of socks. I only carry a small bag in the parks but I'd put extra socks in for those of us who wanted a dry pair at some point during the day. The wet ones went in a ziploc bag.
3. After a full day of wearing the cheapy $1 rain ponchos, we bit the bullet and bought the Disney rain ponchos. That was the best money spent on that trip. The cheapy ones are fine for a quick shower or for staying dry on water rides, but they don't cut it for all-day rain. They stick to your skin and tear easily. The Disney ones are not very expensive (compared to other things at Disney) and we had no trouble getting them replaced for free if they tore (I think we replaced 4 or 5 of them that week). The trickiest thing was spreading them out in the room each night to let them dry -- there were 7 of us in connecting rooms at POP. We each had a rain coat there as well, but they would be soaked in no time -- basically felt like they had gone through the washing machine. We only used them for walking around the resort in the evenings. The ponchos worked better for us (though they're a little more challenging in the bathrooms than a coat would have been).
4. Keep a good attitude and don't let the rain slow you down. I felt like it kept the crowds down quite a bit. I heard several CM's and other guests saying that you could get into a lot of TS restaurants without ADR's that week because so many people just didn't want to go back out in the rain to get to lunch or dinner.
We were fortunate that there was no lightning with the rain so it didn't cause any attraction shut downs. We still got to do almost everything we wanted to do on our trip -- except that I wanted to get to at least 2 fireworks shows that week. Of course it was pouring every night at 9:00 and that's where I drew the line. I was not standing in the rain to watch fireworks. Fortunately, our 2nd to last night there it wasn't raining and we got to see Illuminations.
Despite getting over 12" of rain while we were there, we all had a great time on our trip. I think it was a little better that we didn't know it was going to rain every day before we got there. If we had known, we would have been worried about it. Instead, we just rolled with the punches. You can't control the weather, but you *can* control how you react to it and adapt to it. We leave for Disney in 9 days and right now the long range forecast (that I know will change many times over before we even leave the house) is showing a few hours of rain every day we're going to be there. It doesn't bother me at all. Sometimes I think I'd rather have all-day rain than the high heat and humidity. I'm sure with just a little planning, you will still have a great time even if it rains while you're there. Enjoy!!!!