Rain jacket, ponchos, umbrella, extra plastic bags to keep things dry within your bag/purse, and extra shoes. We went once when it was flooding, and our shoes didn't dry for days (we did not have shoe covers). We rode Hemilich's Chew Chew train 4 times in a row, and when we finally got out, out laps had a pool of water in the poncho.
I bought my clear umbrella, shoe covers arriving today and then...I just decided I didn't want to deal with it. Dapper Day in the rain just wasn't going to cut it for me. Rescheduled my trip for mid-December and will hope I'm not caught in a blizzard leaving home...as Roseanne Roseannadnr would say..."it's always something "...
I've done both WDW and DL in the rain before and it's always been a memorable experience that we still laugh about and it's great for no crowds and you can still have fun. Go out there and enjoy!