Great films where music is a central theme.

I'm a film lover for as long as I can remember. There's nothing like a film that combines my passion for music and film. I'm going to leave out concert films from this, as there are plenty of threads on that. Lets stick to other films - dramas or documentaries - that use music as a central theme, or have it as a key element in the narrative. Here are a few of my own favorites to get the ball rolling.

As it is in Heaven
The Bands Visit
Schultze Gets the Blues
Troubled Water (the Erik Poppe film)
Sweet and Lowdown
Bird
'Round Midnight
I'm Not Here

Documentaries:

Throw Down Your Heart
The Devil and Daniel Johnston
Lets Get Close (Bruce Weber)
Buena Vista Social Club
Bob Dylan: Don't Look Back
Leonard Cohen: I'm Your Man

So it's really could be split into two threads; Narative films and Documentaries. But lets try leaving it open to both, just no concert films. What are some of your favorites?