I just watched *Sweet Bird of Youth *(great acting by Geraldine Page and Ed Begley Sr.; nice body shots of Paul Newman). A few minutes into the film, a piano is playing “Over the Rainbow” in the background . . . a song that we all know was written for *The Wizard of Oz. *So I’m wondering . . . how many other movies contain songs that were composed specifically for a previous movie?
Jack Nicholson singing “Always look on the right side of life” in As Good As It Gets.
“Unchained Melody” was first heard in the film Unchained (1955). In 1990 it became erroneously known as the “Theme from Ghost.”
As Time Goes By from Casablanca, voted by the AFI as the second best film song ever, was written 11 years earlier for the Broadway musical, Everybody’s Welcome.
Malcolm McDowell performs an unorthodox rendition of “Singing in the Rain” in A Clockwork Orange.
And “Singin’ in the Rain” was originally written for The Hollywood Revue of 1929, and was reused in Singin’ in the Rain. Nearly all the songs in Singin’ in the Rain had been written for other movies, with the exception of Make 'Em Laugh, which is a blatant plagiarism of Cole Porter’s Be A Clown, which was written for a movie, too.
Fred Astaire and Ginger Rogers danced to "They Can’t Take That Away from Me** in The Barkleys of Broadway, but the song was introduced (by Fred singing to Ginger) in Shall We Dance.
MGM did a series of musicals using the back catalogs of popular songwriters (Singin’ in the Rain is the best-known). Some of the songs used in these were introduced in films.
The only thing I remember from the movie Punch Drunk Love is that they used the song “He Needs Me” from Altman’s Popeye movie during one scene. Odd enough to stick in my mind, plus I’m a big fan of the Popeye musical.
Singin’ in the Rain was also used in Shanghai Knights.
“White Christmas” first appeared in the film Holiday Inn (1942) when it won a best-song Oscar. Later it inspired the film White Christmas (1954).
And A Clockwork Orange.
“Hooray for Hollywood” has been in dozens of movies after its introduction, usually as an instrumental. One version that had the original song was in The Long Goodbye.
“That’s Entertainment,” written for the movie The Band Wagon was used in a series of documentaries by that name.
Warner Brothers recycled a lot of their film music for their cartoons. You can easily find many examples of standards like “Hooray for Hollywood,” “We’re In the Money,” “The Lady in Red,” “Shuffle Off to Buffalo” (which was the title of one cartoon), and “I Love to Singa” (another cartoon title) in various Merrie Melodies, and there were many more, since the animators were obligated to use them at one point.
I hear that “Singin’ in the Rain” was also used in A Clockwork Orange. But I could be wrong. 
Ah-nuld whistles “Edelweiss” at the beginning of the mall bathroom fight scene in True Lies, a nice nod to both his Austrian heritage and The Sound of Music.
The famous tango “Por Una Cabeza,” composed by Carlos Gardel and used in an Argentine movie in the mid-Thirties, has since appeared Schindler’s List, Scent of a Woman, Delicatessen and True Lies.
“All Star” by Smash Mouth is usually remembered as being in Shrek, but it was originally written for Ben Stiller’s superhero comedy Mystery Men.
Jerry Goldsmith’s theme for the movie Star Trek: The Motion Picture was so good it was reused for the TV show Star Trek: The Next Generation.
Smashing Pumpkins wrote The End Is the Beginning Is the End for the soundtrack of Batman & Robin. It came out with some alternate versions, one of which was called “The Beginning Is the End is the Beginning” and had somewhat different lyrics and was “a more melancholic version.” This version of the song appeared in the trailer for Watchmen.
“Putting on the Ritz” was written for the movie “Putting on the Ritz” but most people can’t hear it without thinking “Young Frankenstein”
Yeah! Wished they’d used it in the movie itself. The lyrics actually fit the movie pretty well. Here’s more on it: Corgan talks 'Watchmen' music