Gambino and Genovese were the only two New York Families that were big enough to be models for the Corleone family. Frank Costello is the 40's mobster who most resembles Vito Corleone, but he was head of the Genovese family.
Thats not true actually there were 5 families during the 40s, which was set up by Salvatore Maranzano and eventually headed up by Lucky Luciano, this was called the Commission of the Five Families of New York. But I actually said Goodfellas which was based in the 60s and 70s and it was the Luccheese Crime Family.
Mastermind still has his question on the board: What mob crime family was represented in the movie Goodfellas? I'm not sure but I believe he may have answered it himself. Was it the Luccheese Family?