It rained a lot on our last trip too (more than usual...the afternoon rains in August are to be expected, but we had several days where it was overcast and then would rain for hours)...
If it's a light steady rain, just slap on your ponchos and have at it!
For heavier squalls that blow through, sometimes the park (especially parts of Magic Kingdom, I've noticed) will flood up. Keep an eye out for good places to camp out until it passes. I have little spots all over the park that I like to hide out with the kid at when heavy rains start up.
For example, at Magic Kingdom, if it starts up and we are in / around Liberty Square, I try to high tail it to the side of the Hall of Presidents. They have a little porch on the side with rockers where you can sit.
Then, once I get the kid settled, I hop over to Sleepy Hollow literally next door) and snag a coffee and a hot chocolate and a funnel cake. We munch on that while we wait for the rain to subside to "poncho" weather again.