‘Laziest Gal in Town’
Performed by Marlene Dietrich (as Charlotte Inwood) in Stage Fright (1950)

‘The Band Played On’
Performed by Laura Elliott (as Miriam Haines) with her friends at the fair in Strangers on a Train (1951)

‘Que será será’
Performed by Doris Day (as Jo McKenna) in The Man Who Knew Too Much (1956)

‘Risseldy Rosseldy’
Nursery rhyme sung by schoolchildren while big black birds gather ominously outside, in The Birds (1963)

What else have I missed?