In '99, we went just before Christmas and found ourselves spending two days under a torrential soaking downpour. (Thank God we were there for a week -- I felt so bad for people there for just three or four days!)
Anyway ... we spent one evening running from awning to awning at Downtown Disney, and then slipped into the movie theaters to see "Stuart Little." The theaters are large and comfortable and we didn't have trouble nabbing a ticket at all (though during busier times of the year, that might be a problem...)
As a rule, I try to avoid doing things at Disney that I can do at home -- things like going to the movies. But when the weather is crummy and your options are limited, those movie theaters can be a blessing!