The only Disney movies that I allow my DD's (ages 2,4) to watch from beginning to end are:
The Many Adventures of Winnie the Pooh
Pooh's Heffalump Movie
Piglet's Big Movie
Mary Poppins
Cinderella
But, my children are familiar with most Disney movies because they've seen the non-scary parts. With the magic of DVD, I just forward past the scary characters/parts. This way they know the characters and songs, but they aren't scared. I've been most successful doing this with:
Dumbo
Snow White
Beauty and the Beast
The Lion King
Pocahontas
Aladdin
The Little Mermaid
Fantasia (including Sorcerer's Apprentice - the girls love Mickey!)
I've had less success with the following because they don't have the songs to help the keep the kids' attention:
Nemo
Toy Story II
Bambi
Disney films, in reality, have many intense, mature, scary parts to them, but with some parental guidance most of them can be enjoyed by all ages.