Because I'm a sane and rational individual, I have begun categorizing songs from Disney movies, and breaking them down into somewhat of a taxonomy. With that short introduction, here are the five categories I have come up with, along with some sub categories that also exist within them. It is important to note that songs can fall in multiple categories.
1. The Exposition Songs
The most common of all songs in a musical, as most real exposition in a musical is done in song. When this is NOT the case, the musical is usually pretty bad (I'm looking at you, Rent) and the story is not progressed through the music, making the addition of the songs... not very important. These songs are categorized by explaining plot points, providing character background, and any other plot important device achieved in song. This family of songs also has two sub categories - the theme, and the montage.
Theme: Pretty self explanatory, an exposition song that explains the theme of the story or provides the thematic tune used throughout. The Muppets is a good example of a recent version of this, as "Life's a Happy Song" is the the background music for most of the movie. "Fathoms Below" from the Little Mermaid is a good example of a thematic song that sets the table for the movie, sort of explaining what the musical will be about.
Montage: Once again, self explanatory. An original song over a montage is extremely common in Disney musicals, as there is usually a large passage of time that occurs in the movie. These songs don't necessarily explain the plot in their song, but become exposition songs when paired with their visual counterparts.
2. The Villain Song
This is Disney I'm talking about here, villain's sing. And it's usually unpleasant. Sometimes this is an exposition song as well, but it doesn't have to be. This is usually a song who's sole purpose is to identify the villain and confirm to the audience that "Yep, that's the bad guy." Ursula's song "Poor Unfortunate Souls" is a great example of this category.
3. The Love Song
Disney movies have love songs. They usually don't advance the plot, they're just love songs. Enjoy them, most of them are pretty good. "Beauty and the Beast" from Beauty and the Beast is probably Disney's greatest example of this category.
4. The Gibberish Song
Disney is kind of well known for making songs without real words. Or, if there are real words, it's impossible to comprehend, or they're presented in a tongue twisting fashion. The premiere example of this category is Bippidy Boppidy Boo from Cinderella. If Lewis Carrol had a stroke while writing, that is the song he would create.
5. The Money Song
A lot of times a song comes up that doesn't really fit these categories, but it's the song heard on the radio, re-released by different artists, or just the one marketed the most. This song is there to make money for the movie. Not always the best song in the movie, but for whatever reason it either becomes the most marketed or is the most marketed by intentional design. "Let it Go" from Frozen is the overkill example of this category.
So there are the five categories of Disney songs. Listening to the Disney station I created on Pandora for Nate, I am able to assign one of these categories to every song I hear, and so far with little or no argument from the wife about what is what. To give an example of how the songs in a movie can break down, I'll assign the songs from The Little Mermaid into their appropriate categories.
Fathoms Below - Exposition, theme category. This song sets up the story, explains the mermaid legend, and even introduces the idea that fisherman are evil.
Part of your World - Exposition song. This song explains Ariel's desire to be human and how she thinks the human world is different, setting up the plot of the entire movie.
Under the Sea - Money song. Possible Exposition. This song is the one every kid loves, the one they sang along to growing up, the one Disney marketed. And rightfully so. I say it is also possibly an exposition song, as the purpose of this song is to explain to Ariel why going to the human world is a bad idea.
Unfortunate Souls - Villain song. Sang by the villain, the song
is dark and doesn't exactly advance the story, just talks about her
ability as a... contract negotiator? Sure, let's go with that.
Les Pouissons - Gibberish song. I know the song is in French and that's a real language, but between the thick accent and the fact his laugh is used to finish a line of rhyme, this is a gibberish song. Doesn't really do anything other than that.
Kiss the Girl - Love song. Money Song. The obligatory Disney love song, it mildly advances the plot, but not by a lot. This is also a money song, as this was another song successfully marketed independent of the movie.
So there's a breakdown of one Disney classic, you can do the same to all others. I'm sure there are more categories out there, but this is what I have so far. Open to debate!
