Usually, around the age of three or four, children are able to sit and watch a movie. At that age most children have the patience to sit in one place for a decent amount of time, but of course each child is different. If your children can sit through a movie or show at home, they'll most likely be okay at the movies. However, if your children get bored fairly quickly and get up and down while watching television, they're probably not ready for the movies.
My husband and I took our little ones to the movies yesterday to see "Frozen" and we had a great time. It's a great movie for the family. It contains a lot of age appropriate action, humour, and great animation for the little ones. We have a six year old, a four year old and an 18 month old. Our 18 month old just sat on my husband's lap and she was good. When we're at home she has no problem watching cartoons or an animated movie with her older sisters, so we knew she would be okay at the movies.
Going to the movies with your children is a fun thing to do as a family, especially if the weather isn't that good. Just make sure it's an age appropriate movie so it's not too complex for your children to understand. Also, avoid movies that contain disturbing images.