Production Studio
Paramount Pictures and Alfran Productions gambled a lot on The Godfather. Paramount wasn't doing too well at the time, and the producers—despite hounding Coppola throughout the process—were actually letting a lot ride on the young, untested director. In the end, it was one of the most successful gambles in cinematic history, and the men responsible were Al Ruddy of Alfran and Robert Evans and Peter Bart of Paramount.
Originally, Paramount didn't want to spend the dough to film the movie in New York City and Sicily—the places where it was set in the book. They wanted to film it for cheap in Kansas City and back in their studios in California, and to change the setting to the present day. But Coppola had other ideas—he made sure that it was filmed on location and set in the 1940s.
The Mafia, however, were not grateful for the attention. The head of the Colombo crime family in New York actually raised money to try to prevent the movie from being made. He claimed that he wasn't really a gangster, and movies like The Godfather just perpetuated negative stereotypes (which is a pretty clever way of trying to protect your criminal enterprise, admittedly). Frank Sinatra opposed the movie, too, since the character of Johnny Fontane was obviously based on him. But it happened, after many tribulations—all detailed in this article from Vanity Fair.