The Godfather is considered by many as one of the best movies ever filmed. The main success of this movie could be referred to three factors: The great story, The great directing, and the great acting cast. Music is also amazing, inspiring, and still heard till now as a classic.
The Godfather movie had many aspects that weren't either planned by the original story or script. Even Francis Ford Coppola (the director) was surprised and amazed many times by his actors' improvisations. The final movie version we saw was a combination of many of these improvisations lead by actors and Coppola himself who eventually decided to keep them in scenes.
1- Lenny Montana who played (Luca Brasi) was so nervous working with Marlon Brando, when they were to make their first scene together he skipped some lines due to nervousness and said some others wrong. Francis Ford Coppola (the director) liked this genuine nervousness and made use of it in the final cut where he looked so nervous addressing Don Corleone at his daughter's wedding.
2- Francis Ford Coppola used a real horse head in the scene where Jack Woltz (played by John Marley) woke up to find the head of his slaughtered beloved horse (Khartoom). Coppola thought this might make his panic more real and it happened where Jack Woltz kept screaming insanely. Of course, activists of animal rights protested for this act and Coppola stated later that he got the head from a dog farm where many horses were slaughtered daily to feed the dogs.
3- Marlon Brando wanted to look like a real bulldog so he stuffed his cheeks with metal and cotton parts to give him this abnormal wide jaw appearance. The device he wore was made by a dentist and it is being currently shown at the American Museum of the Moving Image.
4- James Caan improvised the part where he throws the F.B.I. photographer to the ground and hence breaking his camera. He also had the idea of throwing him money as a compensation for the camera as his culture states to pay for the things he breaks.
5- The cat that Marlon Brando held in the opening scene was not even in the script, it was a stray cat coppola has found at the filming theater and decided to put it on the first scene as many other scenes that were improvised. The cat added value to Don Corleone's character as a nice animal loving man besides his vicious personality when it comes to business.
6- At the beginning, Paramount Pictures didn't want Francis Ford Coppola to direct the movie as he was famous for exceeding the budget and delivering late on time. But in this movie, Coppola delivered just in 62 days and went below the allowed budget.
7- Where Don Corleone smacked Johnny Fontane on the face, it wasn't in the original script. Johnny Fontane was surprised and didn't know whether to cry or laugh and so he got this mixed expression we all saw on the screen. Coppola liked this expression and decided to keep the smack in the movie.
8- The scene where Sonny beats up Carlo (Connie's husband) took four days to shoot and the background had to be hidden by a big van to hide modern cars and ads that weren't matching the timeline of the movie. Caan's beating Carlo with the garbage can was also improvised and wasn't in the original script.
9- Don Vito Corleone's deep and weak voice was inspired by real-life mobster (Frank Costello). Marlon Brando liked the tone of his voice after seeing him on television for trial and decided to imitate him.
10- The tears in Marlon Brando's eyes were real in the hospital scene when Michael visits him and tells him he's gonna keep him safe.
11- Marlon Brando did not memorize his script much and used cue cards telling him what to say behind the camera during most of the film.
12- Oranges were always related to a death in Corleone's family. Whenever oranges appeared, there was someone to die. Even when Don Corleone dies, he was playing with his grandson in his orange farm moments before he fell dead.
13- Al Pacino didn't go to the Academy Awards after being nominated for best actor in a supporting rule. He was so angry because he wanted to be nominated for a leading rule stating that he had more scenes filmed than Marlon Brando himself who won the Oscar for his rule.
14- Paramount Pictures didn't like the darkness and low light intensity in many scenes and the cinematographer Gordon Willis was given a nickname "The Prince of Darkness". Coppola had to convince Paramount that darkness was necessary to resemble the reality of Corleone's family shadiness.
15- Orson Welles (from Citizen Kane) tried to earn the rule of Vito Corleone but Coppola let him down as he was very satisfied with selecting Marlon Brando for the rule.
16- Francis Ford Coppola was in debt to Warner Bros when he decided to film that movie in order to pay his debts.
17- The most famous quote in the movie is: "I'm gonna make him an offer he can't refuse". It was selected by the American Film Institute as number 2 for the top 100 movie quotes. Number 1 goes to "Frankly, my dear, I don't give a damn" from the movie (Gone with the Wind).
18- Talia Shire who played (Connie) is Coppola's sister in real life. He didn't want to give her audition at the beginning because he thought she is too beautiful to play the rule.
19- Talia Shire wasn't the only Coppola in the movie, actually he might has brought his whole family to act several rules in the movie. His mother, Italia Coppola, served as an extra in the restaurant meeting, his 20- father, Carmine Coppola, played piano in the Mattress sequence and, he composed the music, his sons Gian-Carlo Coppola and Roman Coppola, can be seen in background in the scene where Sonny beats up Carlo, and his daughter, Sofia Coppola, is the baby, Michael Rizzi, in the baptism (she was three weeks old at the time of shooting) and she later on played Michael Corleone's daughter in the third part of the movie.
20- Paramount was in severe financial crisis upon shooting the movie and so they asked Coppola to make the movie explicitly violent to make a big hit out of it to save their financial position.