Many actors have a sliding doors moment in their career when they pass up a choice role in a soon-to-be iconic movie. For some, it isn't a huge deal. Denzel Washington, for example, already had two Oscar nominations and one win under his belt by the time he decided he didn't want to star in David Fincher's "Se7en." Sure, he later came to regret turning away one of the defining films of the '90s, but he was already an established star and would be just fine without it. That isn't always the case when an actor hasn't quite built up the body of work to go around rejecting great parts –- just take Henry Winkler and Danny Zuko in "Grease."

Winkler was virtual unknown when he won the chance to play Fonzie on "Happy Days." Arthur "The Fonz" Fonzarelli started out as a minor supporting character but quickly...