ADDENDUM (added 2/10/12):
I am currently reading Julie Andrews' memoir "Home" and she writes details of her stage performances in the Broadway and London versions of "My Fair Lady". She mentions how strict Rex and some producers were in keeping the script identical with the the original play, "Pygmalion" by Bernard Shaw. Even though a beautiful song was written for Julie in which Eliza expresses her feelings for Professor Higgins, it was cut in order to stay true to the original: the characters never once speak of love. Instead, they wrote "I Could've Danced all Night" which still conveys Eliza's emotions but without mentioning the word. I think this is very interesting because I, myself, didn't really see this film as a love story.
Another song was cut and used in the strikingly similar story, "Gigi": "Say a Prayer for Me Tonight".
Warner Bros. needed a big name for the marquee and called upon Audrey Hepburn for this role over Julie Andrews even though she was the woman who made it famous. Audrey and Julie became friends and one day, Audrey said to her, "Julie, you should have done the role... but I didn't have the guts to turn it down."