In the 1977 film MACARTHUR, during an early scene wherein MacArthur and his family are hiding in a bunker, he dances/marches around the room with his young child, as the Goldsmith title March plays - in a somewhat tinny version - on a record player seen in the background.
The previously mentioned The Prize by Goldsmith shows up as muzak in his score for Coma. Bond & Kendall note "proof that one decade's hit movie theme is another's muzak".
William's Earthquake has quite a bit of thematic-souce-muzak as well. All of it 'muy bueno' IMO.
Obviously a common occurrence. A favorite joke occurs in Rozsa's TIP ON A DEAD JOCKEY, when Robert Taylor bangs out music from SOMETHING OF VALUE on the piano after a casual reference to the Mau Mau.
I recently watched the new Kino Blu-ray release of Mancini's MOMENT TO MOMENT (1965), a nearly monothematic score in which the theme is heard often as source music, and even serves as a plot device in revealing a clue to the story's mystery.
In PETER IBBETSON (1935) both Dickie Moore and Gary Cooper whistle a signature theme from the film's score.