Not exactly sung, but they do have a common melody: checkout Sinfonie Nr. 3 in F-Dur, Op. 90 – III. Poco allegretto by Johannes Brahms and then Love Of My Life by Santana (ft. Dave Matthews)
“do your ears hang low” and the “do you hear the people sing” song form les miserable have really similar tunes – they sound good when sung at the same time
A few things use the traditional Shaker song “Simple Gifts.” Most notably: the Protestant hymn “Lord of the Dance,” the old TWA commercial, and “The Greatest Man Who Ever Lived” by Weezer.