Cool thread! I'm newish to the forum and just discovered it. Thanks for all the great suggestions.
FYI, Hilary and Jackie, mentioned earlier in this thread, is about the Du Pre' sisters.
Departures is a Japanese film about a cellist who gives up a classical music career, returns to the small town home he grew up in and finds a job preparing the dead for burial. The job, the instrument, classical music, the father who abandoned him, will all play a part in his enlightenment. The film is overly ambitious, but charming and at times profound, and there is much beautiful music, and beautiful silences.
Fingers stars Harvey Keitel as a mob enforcer who is also an aspiring concert pianist. Yep.
First Name Carmen is a movie by Jean Luc Godard that includes a string quartet and much Beethoven (the late quartets). More or less about a gang that robs banks to finance a movie production that will be the cover for a kidnapping; one of of the gang has a weird movie director uncle, played by Godard, who is to direct the movie, but at times appears to be directing First Name Carmen...
Truly Madly Deeply is a wry comedy/drama, with Alan Rickman as a cellist whose ghost returns to his grieving wife. Roger Ebert called it "'Ghost' for adults". The cello music is mostly (or maybe all?) Bach.