Kiddie Records Weekly is still my #1 place to go for kids' audio stories.  They have many Walt Disney stories to download for free or listen to on their site.  They also share some of their stories on Kiddie Records Weekly YouTube channel. 

This isn't a complete list of Walt Disney stories so look around Kiddie Records to find even more!

2006
week 2 - The Adventures of Ichabod and Mr. Toad
week 10 - The Flying Mouse
week 45 - Elmer Elephant
week 48 - The Whale Who Wanted to Sing at the Met



2009
week 3 - Dumbo
week 7 - Cinderella
week 20 - Mickey and the Beanstalk
week 44 - Little Toot

   
More Golden Age Classics
pg. 2
Bambi
Ferdinand the Bull
pg. 3
Peter Pan
Lady and the Tramp




Kiddie Records Weekly YouTube 
Goliath II
The Ugly Dachshund
Three Little Pigs