We bought these super lightweight rain jackets from land's End for our kids. They fit better and are more comfortable for them than ponchos. They also fold up into a little built in pouch, and fold even smaller than ponchos. If they made them in my size, I would get one for myself too!
If you take a stroller, having a stroller cover, or using a poncho or something to keep the stroller dry is a must. You can throw all your stuff in there to keep it dry. And it's pretty miserable to have a child sitting in a wet, uncomfortable stroller seat.
I tend to wear flip flops to the parks, especially if it looks like rain. For anyone wearing sneakers, I try to bring a thin pair of flip flops along. At the first drop of rain, they can change into the flip flops and stash the socks and sneakers in a plastic bag until the rain stops. Wet socks and sneakers are awful.
Definitely make use of the Disney plastic bags! I keep a couple on hand and can toss our bags or whatever in them to keep them dry. We got caught in the rain when we had some photos from a character meal with us, and I put them in one bag, then turned that bag upside down and put it into another bag, so it was super protected from the rain.
Ziploc bags are another really good thing to have. I keep our autograph books in a Ziploc bag at all time when we're carrying them around. They've been saved from rain, water bottle leaks, and spills numerous times by the bag. They're also good for cell phones, or a spare change of clothes.