DD6 is very hit or miss with movies. We did not allow screen time until she was 3, but now we don't limit it, she has always done a good job of self-regulating.
DD is very sensitive and there are many movies she does not enjoy (anything Muppets, anything dinosaur related--she starts thinking about their extinction, and always ends up sad and crying), Brave and quite a few other Disney movies.
Some of her favorites are Charlotte's Web (the one with Dakota Fanning), Mr Poppers Penguins, Mary Poppins, Annie, and Frozen. She watches very little TV, pretty much only My Little Pony and Fresh Beat Band. Occasionally, she watches nature documentaries...she loved Flight of the Butterflies which was at our Imax theater recently.
I saw a few great suggestions by PP, I have now added Matilda and Parent Trap to our Netflix queue.
I love Hayao Miyazaki's movies, but so far her sensitivities are still keeping these off-limits. She did watch Arrietty, and for the most part liked it, but there were a few parts that we had to fast-forward through. She only gave Ponyo 5 minutes before asking if we could turn it off.