From reading the original tales I can conclude that..

Although there are certain themes and issues that are already present in the original stories, (royalty, good vs evil, vulnerable female protagonist figure), Disney consistently include themes of their own which do appear to be signatures of the studio.

• Enchanted animal or objects as friends add to the element of fantasy in the films, as well as being able to let a lot more depth of the protagonists' character be explored.
• Representation of women - traditional, negative- women in Disney animations are either vulnerable and weak, home makers and house keepers, cooking and cleaning after people, dependent, yet beautiful and dainty, or they are evil, controlling, psychopathic, desperate for wealth, youth, beauty and attention.
• The antagonist in Disney animations is predominantly actually part of the family of the protagonists. - Evil Step mother, Uncle Scar, etc
• A broken home/single parent family - appears to be a very Disney stamp on the stories, sometimes finding a mother/father figure of their missing parent in another character - Rafiki shows Simba his father is in the sky, Mrs Potts mothers Belle.
• Love and romance, - emphasized much more in Disney animations than the original stories, love is represented as a dream to aspire to - very idealic.
  
• Adventurous fun developing friendships is also a theme which Disney force upon each of the tales in order to make them family friendly.

These are conventions which the Disney audience has learned to expect from Disney animations, without them the success of the films may be effected dramatically. Disney make conscious decisions to cut out any themes and issues which may take away from the happy, adventurous and romantic tone to their animations, which give a consistency to their work.
The Lion King was the first Disney animation to be written from an original idea. It's controversy with the not-so-suitable for children scene of Mufasa's death was a risk. However the bright and exciting African theme with catchy songs and exciting friendships and subplots managed to make it so successful that Disney took it out of the American cinemas in order to re-release it at Thanksgiving in order to make even more money.
Is this because it was fresh and new or because it followed the same themes and issues expected from it's audience? I will look at the success of the other Disney films using Box Office Mojo.