Critics and audiences consider Marlon Brando to be one of the greatest actors of all time, and Don Vito Corleone proved to be one of his greatest roles—maybe the greatest. It roped him a Best Actor Oscar, in any case. Francis Ford Coppola said that once he convinced Brando that the film wouldn't glorify the mafia, Brando started transforming into Vito Corleone right before his eyes, popping cotton balls in his mouth and adapting the famous voice he used for the Don.
Vito Corleone is the head of one of the "five families" of New York, the five local branches of the mafia (although the word "mafia" is never used in the movie itself). Technically speaking, he may not be the most moral guy in the world—letting his henchmen hack off a horse's head and put it in a movie producer's bed, and so on—but he apparently has a few principles.
For instance, he says he won't murder the men who attacked a friend's daughter because it's out of proportion to the crime committed. He'll only beat them up just as badly. Also, and more importantly for the plot, Vito refuses to deal drugs or help other Mafiosi do it, which leads to an assassination attempt that almost kills him.
Throughout the rest of the movie, the Godfather is kind of out of commission. Sonny is the acting Don for a while, until he gets whacked, and Vito has to make peace with the other bosses. He survives long enough to help Michael identify the man who is trying to betray them to their main rival, Don Barzini, before dying in a nice, peaceful manner, while playing with one of his grandkids in a tomato garden.
Master of Puppets
Vito Corleone is obviously one of the two most important characters in the film—but is he really the main character? Or is Michael? We follow Michael in our "Hero's Journey" section, but, hey, the movie is named after Vito's character. (Or, wait… since Michael becomes the new Godfather at the end, it might be named after him, or both of them. So scratch that.)
Even though he's a criminal and therefore a "bad guy," Vito is more complicated than he appears. He justifies what he does and doesn't seem to regret it, but he recognizes that it's not the best. He tells Michael:
"I work my whole life, I don't apologize, to take care of my family. And I refused to be a fool dancing on the strings held by all of those big shots. That's my life, I don't apologize for that. But I always thought that when it was your time, that you would be the one to hold the strings. Senator Corleone, Governor Corleone, something."
It seems, though, that Michael ends up going in a different direction from his father. It's seems that he's ditching Vito's principles and sense of justice, murdering people who weren't really responsible for betraying him or killing his brother in the process of taking revenge (like the woman who gets murdered along with one of the Dons Michael has killed, or, to a lesser extent, Moe Greene). Vito represents the way of doing "business" in the past, in the Old World, whereas Michael is trying to ride the violent wave of the future.
Also, The Godfather Part II gives a great glimpse into Vito's backstory (this time played, as a young man, by Robert DeNiro) and helps explain how he became the man he is in the first movie.