I've seen a lot of movies. I've seen a lot of movies that deal with music. So, here are my favorites. My only parameter: no documentaries - I might save that idea for a future post.
1) Sweet and Lowdown
Even though this may be some of the worst musical direction considering Sean Penn's playing is terribly off the entire film, the story is great, the music is better (nods to Howard Alden), and even though Emmet Ray is not a real person, the film brought Django Reinhardt into the public eye again.
2) Orfeu Negro (Black Orpheus)
This is what you get when you cross contemporary Brazil (in 1959) during Carnaval, Greek legend, and some amazing bossa nova by Jobim and Bonfa (music) and de Moraes (lyrics). At times it is quite far-fetched, as in the prominent role of Death (while not as prominent as Death in Bill and Ted's Bogus Journey). Nevertheless, it has some really poignant moments, especially the children who think Orpheus' guitar causes the sun to rise. Beautiful.
3) Les Parapluies de Cherbourg (The Umbrellas of Cherbourg)
The only true musical to make my list! A visual and sonic tour de force, Jacques Demy's jazz musical starring Catherine Deneuve and Nino Castelnuovo is entirely sung. A simple story-arc that deals with class differences, young love, and the personal stress caused by war, the film elegantly displays the ebb and flow of the character's emotions. Michel Legrand's music is the key and his tune "I Will Wait For You," possibly my favorite melody of all time, is a good example of how to make an otherwise possibly blase story come to life.
Maybe it's because I didn't watch this at a private screening at Dustin Hoffman's house that I don't think this movie blew like some people. For us laypeople, this movie, like the previous one, contains about as simple of a story-arc as possible: a tale of lost love and possible love, of hope and courage, of chance meetings and taking action. The music is not the most mind-blowing music ever made, but that's the point. It's passionate, believable, and quite good! The clip I've included is pretty poor quality but its the best scene in the movie. It really gets at some studio dynamics that are all too real. Also, their Oscar acceptance speech was amazing. See a review of that here.
5) Get Over It
You knew that a teen comedy had to creep in here sooner than later! While technically not "about" music, this movie is basically a musical, and the last 20 or so minutes is basically a movie about a musical about a musical about a play. One of the more underrated teen flicks, this movie is self-aware, WAY over-the-top, and hilarious. Also, you can't go wrong with a cast that includes Martin Short, Kirsten Dunst, Ed Begley Jr., and two people contending for the title of worst actor of all time: Sisqo and Colin Hanks.
Shine (maybe the movie with the best musical direction ever) and another teen comedy, That Thing You Do.
You'll notice I didn't include any mockumentaries like Spinal Tap or A Mighty Wind. No real reason, they're pretty good. What would you include?