Paul McCartney penned Hey Jude while sitting on a train, on his way to visit Julian Lennon to help him through his parents' (John and Cynthia's) divorce. McCartney originally titled it "Hey Jules" (after Julian), but decided to change it to "Hey Jude".
Upon returning to the studio, McCartney showed the song to John Lennon. McCartney mentioned that he wasn't done with it; he wanted to get rid of the lyric "the movement you need is on your shoulders".
"Are you kidding?" Lennon exclaimed, "that's the best part!"
The rest, as they say, is history.