Non-Singing Voice: Marni Nixon did most of Audrey Hepburn's singing for the movie; this is at least partially responsible for the Award Snub mentioned above. And no, Marni Nixon's name appeared nowhere in the original credits.
However, when video of Hepburn's original vocal performances was released in the 1990's, many fans found Nixon's overdubbing to be completely unnecessary.
Also, Jeremy Brett as Freddy was dubbed by Bill Shirley (AKA Roger (singing) and Prince Philip).
Out of all of them, Brett was the one who could sing. Look him up on YouTube. But his singing voice was thought too mature for Freddy.
Rex Harrison couldn't actually sing either, but he developed a sort of recitative to compensate.