First ones that come to mind are Here's To You - used in various films, but I have to admit to knowing it from The Life Aquatic with Steve Zissou rather than Sacco & Vanzetti or Germany in Autumn.
And Some Velvet Morning - I didn't really love Morvern Callar, took me a while to look up what the film was called, but think it was the first time I heard Some Velvet Morning, which is definitely a song that stays with you.