@geoffkait -Good call on The Third Man, zither by Anton Karas. I used to love that movie and the score is whimsical against very darkly shot (literally and figuratively) scenes.
Movies employing music in a great way.
I find certain directors are more aware of great music, and of how to integrate it into their films, than are others. Jim Jarmusch, Martin Scorsese, The Coen Brothers, and David Lynch come to mind. But maybe my favorite use of music is in the movie The Last Picture Show; lots of Hank Williams on the radio in the old pickup truck driven in the movie, perfectly reflecting the grim, dying small-town and sepia-hued Texas landscape.