Sergio Leone
Italian director Sergio Leone was the original director of the film. He turned it down because he felt that it glorified the mafia. He eventually directed a mob film of his own, Once Upon a Time in America, and got an Oscar nomination for Best Director.
Sylvester Stallone
Sylvester Stallone wanted to be on The Godfather cast badly. He auditioned for the role of Carlo and Paulie. Apparently, he "wasn't Italian enough." Eventually, he went on to snag the role of Rocky and was launched into superstardom. Paramount tried to get him to star in The Godfather: Part III but he turned it down.