The Famous Cannoli
Never mind The Godfather's incredible storytelling and fantastic theatrics, the most memorable part of the movie is easily the line: "Leave the gun. Take the cannoli." This line was completely improvised, which makes it even better.
Paramount vs Coppola
Coppola wasn't entirely wrong for being skeptical of Paramount. In truth, they really were trying to fire him! They ended up being very lucky that they didn't. He finished the movie under budget and created the franchise that The Godfather is today.