The novel, "The Godfather" by Mario Puzo was originally published in 1969 by G. P. Putnam's Sons. It remained on "The New York Times" Best Seller list for 67 weeks and sold over nine million copies in two years. The novel details the story of a fictional Mafia family in New York City headed by Vito Corleone. Unsurprisingly, it uses the word "Mafia" dozens of times.

Not so with the film of the same name.

Francis Ford Coppola directed the 1972 film "The Godfather" based on Puzo's novel. Coppola and Puzo co-wrote the screenplay,

However, the Italian-American Civil Rights League, led by mobster Joseph Colombo, wanted all uses of the words "Mafia" and "Cosa Nostra" to be removed from the script, in addition to feeling that the film emphasized stereotypes about Italian-Americans. Coppola claimed that Puzo's screenplay only contained two instances of the word "Mafia" being used, while "Cosa Nostra" was not used at all. Those two uses were removed and replaced with other terms, which Coppola felt did not change the story at all. The league eventually gave its support for the script.

So, in the end, "The Godfather" does not mention "Mafia" at all!

More Info: en.wikipedia.org