Wear shoes that dry out easily and have traction on wet ground. I wear Teva sandals. If it looks like it will rain all day, bring a back up pair of shoes and plastic bags for wrapping up wet shoes. Wear clothing that won't become see-through in wet weather. Bring baggies for your phones and anything else you don't want soaked. We have tried ponchos in the past, but they were too cumbersome and hot for us. We decided wet clothing was better.
We do look for indoor attractions, stores, restaurants, etc to escape the rain, but we don't let the weather get us down. MK is actually a pretty good place for a rainy day. Lots of ways to pop in and out of the rain there, and lines can be shorter. We found Epcot to be much worse in the rain. Things are more spread out and the pavement fills with water quickly. We haven't had rain at AK or HS, but I imagine those parks might be a bit trickier than MK, too. I would probably spend a good deal of time taking in shows at HS if it was a rainy day, though.
These towels are a must have on a rainy day (or a hot, sweaty day). They wick away moisture quickly and dry out quickly, too. They come in a variety of sizes.
Baseball caps can help keep the rain off your face. If you have long hair, a pony tail works better than having wet hair hanging down around your face and on your shoulders.
We've been in tornado warnings, gale warnings, and had quite a few full days of rain during our trips. The very first bad weather day we experienced was the worst, but it taught us what not to do. The most miserable aspect was our feet, so keeping them as dry and comfortable as possible is our main priority in rainy weather now.
