In 1937, Walt Disney released the first feature-length animated film in the English-speaking world and the first feature film made completely with hand-drawn animation. However, it wasn't, as many claim, the first feature-length animated film ever. Foreign examples predating Snow White and the Seven Dwarfs and using other kinds of animation include Argentina's The Apostle (combining hand-drawn with cutout animation) in 1917, Germany's The Adventures of Prince Achmed (done with silhouette animation) in 1926, and The Soviet Union's The New Gulliver (done with Stop Motion) in 1935.
This category does not include productions from Walt Disney Animation's sister studios Pixar and Blue Sky, nor does it include every animated feature released by Disney (such as the Direct to Video Sequels and other films created by Disneytoon Studios, Studio Ghibli dubs, animated films made under a different Disney banner such as The Nightmare Before Christmas, which was made under Touchstone Pictures, or animated films distributed by Disney but produced by non-Disney studios). There don't seem to be any hard-and-fast rules as to which movies get to be part of the canon and which don't, but generally, the canon films have a big budget and are made by the Disney feature animation unit (live-action/animation hybrids like Song of the South and Mary Poppins tend not to count unless the animation is the bulk of the film, as in The Three Caballeros, Fun and Fancy Free or Melody Time). The Other Wiki has a set of lists for both the canon and non-canon films.
See also Disneytoon Studios, Disney Princess, Enchanted (an Affectionate Parody of Disney's own films), Kingdom Hearts, a video game series which also seems to follow the rule of only using canonical characters from nearly all of these films (and then some!), or House of Mouse which represents almost every canonical movie up to 2001 with at least a cameo appearance. Once Upon a Time is a live-action fairy tale series shown on Disney-owned ABC, with versions of the fairy tale characters heavily and obviously indebted to the Disney animated film versions. Descendants is a similar all-DAC crossover Disney Channel Original Movie, featuring the offspring of classic Disney characters in a live-action musical. The Disney Live-Action Remakes refers to a series of films that remake DAC films in live-action format.
Who Framed Roger Rabbit and The Nightmare Before Christmas were both produced and released by Disney under its Touchstone Pictures banner (the latter's 3D re-releases were under the Disney banner). Compare the works of former Disney animator Don Bluth, as well as the two feature length animated films made by Fleischer Studios.
For notable Disney staff, go here.
The list of all the films in the canon (plus upcoming films, related franchises, cancelled films, and live-action remakes) can be found on this Recap page.
All of them have been pitted together in a competitive tournament-style poll as the subject of the podcast Mouse Madness.