Many great suggestions, but I think that the distinction between “music movie” and “movie music” has gotten blurred. Some great (best?) music movies not mentioned yet:
“Thirty Two Short Films About Glenn Gould”. Brilliant
“I Called Him Morgan”. Documentary film about the great Jazz trumpeter Lee Morgan.
“A Great Day In Harlem”
”The Benny Goodman Story”.
”Fantasia”. While some might argue that the central theme here is the classic Disney animation, I would argue that it is the music, some of the greatest Classical works ever composed, that is.
“Amazing Grace”. The great Aretha Franklin.
“Lady Sings The Blues”. Billie Holiday.
“Straight No Chaser”. Monk.
Some great movie music:
”On The Waterfront”. Another fantastic Bernstein score. Not a lot of it, but I can’t think of another score that does a better job of serving the film’s plot.
”The Pawn Broker”. Great Quincy Jones score.
“Elevator To The Gallows”. Miles.
“The Mambo Kings”
“Manhattan”. Classic Woody Allen.
“Ivan The Terrible”. Another great Prokofiev score.
“The Adventures Of Robin Hood”, “Sea Hawk”, and just about any other score by Korngold.
