Surprisingly, the word "mafia" isn't used in The Godfather. Additionally, by pure coincidence, Al Pacino's grandparents actually immigrated from Corleone, Sicily, to America (the same town the Corleones are from). (Source)

No one really used the term "Godfather" to describe a mob boss until Mario Puzo used it in his book. (Source)

Brando wore a mouthpiece made by his dentist to achieve the "bulldog" look he wanted Don Corleone to have. Also, the cat he's petting in the first scene wasn't called for in the script—it was a stray he found on the lot. (Source)

Actor John Marley wasn't informed he would be waking up next to a real horse's head (they got it from a dog food company). His scream of surprise is real. Plus, for Sonny's death scene, James Caan's suit was affixed with 127 fake blood pouches. Also, Caan researched his role by hanging out with actual members of the mafia. (Source)

Barack Obama said The Godfather was his favorite movie of all time. (Source)

Cinematographer Gordon Willis insisted that all shots in the movie should feel like they were coming from a person's point of view. The one exception is the aerial view after Don Corleone is shot in the street. According to Coppola, that scene is from God's point of view. Also, the oranges seen in that shot, and others, signify the threat of imminent death (apparently). (Source)

In Balzac's Le Pere Goriot, the criminal mastermind Vautrin says, "In that case, I will make you an offer that no one would decline." This seems to be the forerunner of The Godfather's "I'm going to make him an offer he can't refuse." (Source)