There's so many great music related movies, and I agree with a bunch that have been previously mentioned. The Last Waltz is probably the greatest concert film ever. And Let It Be is a fantastic look at The Beatles, warts and all, as they worked up material for an album and a live show.
As for an actual feature film? I'm surprised nobody mentioned it, but I have to go with Still Crazy. It's probably the most representative film of what it's actually like to be in a band. And the cast is absolutely amazing! Bill Nighy, Stephen Rea and Billy Connolly are all fantastic in the film. But I found that English singer/actor Jimmy Nail, who played the bass player, Les, was the soul of that movie. If you can, do check out this movie.