Martin Scorsese is famous for his collaborations with Robert De Niro and Leonardo DiCaprio, and the first feature-length film with all three, “Killers of the Flower Moon,” has become a critical and commercial success. It’s not unusual for a director to find a “favorite” actor and form a successful relationship. In fact, this practice goes back to the beginning of the industry.

In 1912, pioneering filmmaker D.W. Griffith cast 18-year-old Lillian Gish in his short film “An Unseen Enemy,” and the two worked on more than 40 short and feature-length productions over the next decade. One of the most famous scenes from the silent era is in their film “Way Down East,” in which Gish floats unconscious on an ice floe; she had lifelong nerve damage in several fingers as a result of her performance in that scene.

During the Golden Age of Hollywood, there were quite a few famous collaborations,...