I mean "music not specifically written for the soundtrack".
I watched Buffalo '66 a while ago, and the unlikely combination of Yes' "Heart of the Sunrise" and an imaginary murder/suicide/night-club scene had my chin on my chest.
Other favourites would be Rhapsody in Blue over the last few seconds of "Manhattan" - always brings a lump to the throat
"Summer Wind" as the outro to "The Pope of Greenwich Village"
And Scorsese can usually be relied upon to match sound to image in a memorable way.