The Godfather
The name "the Godfather" has a symbolic ring to it. Just the word itself, comprising "God" and "Father," seems to say a lot: It conveys power, the sense of a patriarch or maybe of a wrathful deity.
In Christian tradition, godparents are the people who will assume legal guardianship of their godchildren in case the actual parents die. (It's largely an honorary function, nowadays.) In the movie, "The Godfather" is more a guardian of both his literal and symbolic godchildren's interests: He protects them by going around the law, demanding their eternal loyalty. All they have to do is agree to return the favor—by means illegal or legal.
There is something oddly god-like about this relationship, since it bears a similarity to the way an ancient Roman deity might reward his or her devotees in exchange for a sacrifice. The Godfather is a kind of puppet-master too—trying to pull strings that other people are holding (this is depicted in the logo for the film's title, where a hand pulls marionette strings attached to the words).
Interestingly, no one in the mafia called the head Don of a family "Godfather" until after Puzo did it in his book. The head of a mafia family was just called the "boss of the bosses," or capo di tutti capi in Italian.