In the fall of 1996, a $30-million Hollywood production almost ground to a halt because of facial hair. As producer Art Linson recounted in his 2002 memoir, "What Just Happened?," Alec Baldwin surprised everyone when he showed up to film "The Edge" (1997), a man-against-nature thriller, with an overgrown beard. A profanity-laced debate ensued between producer, star, agent and studio executives.

Finally it came down to this: The execs, who had already sunk millions into the production, wouldn't shoot the picture with...