Believe it or not but MK actually does have a lot of indoor rides. It's just getting to them that is harder. I didn't believe it until we were there one time and it was pretty rainy - when everybody was leaving we stayed and enjoyed rides without lines - It's a Small World, Winnie the Pooh, Peter Pan, Pirates, Space Mountain, Buzz, Teacups you can do in the rain as long as it's not a sidewards rain, Haunted Mansion, Hall of President's, Country Bear and any other shows and even the character area across from Pooh you'll find characters because they are under cover.
Then there's the shops on Main Street - did you know you can start at one end and go straight through to the other end? Great for a rainy time period.
And if you love Epcot World Showcase and don't ever get a chance to go to the Imagineering part of Epcot - a rainy day is a great day for that too because almost all of that stuff is indoors and you can spend hours at some of that stuff.