Just first thoughts off the top of my head....one of my early memories is the great music in The Jungle Book, especially this one which still stands up as a classic..
I Wanna Be Like You

..and in terms of directly influencing me personally, a more recent one is the scene in Cold Mountain (not the greatest film but with some great music) where they are singing Sacred Harp in the church, as this led me to this fantastic form of singing which is a big part of my life five years later.
Sacred Harp singing in Cold Mountain

And O Brother, of course, which fostered my interest in bluegrass and old-timey music in general and the banjo in particular - especially as I'd been an AKUS fan for a few years already, so enjoyed the fact that the marvellous Dan Tyminski provided the voice for George Clooney. But I think this bluesy song from Chris Thomas King was particularly affecting in the film.
Hard Time Killing Floor Blues