I can't add very much that is specific, but presumably the film about Woody Guthrie starring David Carradine as Woody Guthrie (was it called "Bound for Glory"?) featured a few of Guthrie's songs.

Oh and I remember first hearing "Down in the Valley" on "Stir Crazy"), a comedy film set mainly in prison starring Gene Wilder and Richard Prior, in which the song was sung by one prisoner in the jail and joined in by others. Mind you it was several years before I discovered the name of the song (I thought it might be called "Birmingham Jail", and eventually recognised the tune on musical CD-ROM available from www.traditionalmusic.co.uk). I think I have heard it called Birmingham Jail.

Among the worst singing I have heard in films are (a) John Wayne singing "Streets of Laredo" (b) An actress (perhaps Shirley Jones, later of the Partridge Family?) singing a song to the tune of Greensleeves but to different words (the only bit I can remember, mercifully is "And build me a home in the meadow" or similar.

Come to think of it, it is remarkable how few folk songs, even on the more liberal interpretation, have been suggested so far as occurring in films. Either people's memory is poor, or as I suspect, relatively few folk songs have been used in films. Presumably as films cost millions to make, there is no point in saving a few hundred or thousand on royalties by using traditional and hence non-copyright material. I suppose it makes sense to pay someone to write an appropriate song or songs for the type of film, which may sound like a traditional song even if it is not.

I suppose one could extend the scope of this thread a little bit by listing folk songs or tunes used in TV or radio programs. One of my favourite TV programs (of the 1970s) was "When the Boat Comes In", a drama set mainly in the North-east of England from about the early 20th century (before the 1st world war) and ending at the Spanish Civil War (1936-39) with the death of the main character, Jack Ford (played by that very versatile actor, James Bolam). As you might expect, the theme song was "When the Boat Comes in", sung I think by Alex Glasgow.