We had one rainy afternoon - and they offered a matinee of Disney Dreams that day. So we did the matinee - which freed up our evening when there are a lot more entertainment options. We also booked our next cruise. Gotta do that sometime....
They run movies in the movie theatre. They have a lot of programming - my husband and son learned to draw Mickey Mouse. The kids clubs are inside - as is the spa - so you can drop your kids off and enjoy the Rainforest Room. You can nap in your room - and then dance the night away. Character greets. And of course, eat. My daughter missed the "fancy dress up dinner" at Tritons because she was in the kids club - so the next day we all went back and dressed for lunch. Drinks in the prominade lounge - where rum drinks are perfect by the pool, martini's are great for a rainy pre-dinner drink in the lounge. Of course, there are few things more cruise like than a good book - and there were lots of places you could sit inside and read and people watch.
In fact, even on sunny days, inside the ship was just as busy as the deck. We saw few people sitting around on lawn chairs by the pool (but we were always by the pool during unpopular times - morning and when we were in port).