20's - 40's. Genovese, in whatever incarnation.

Late 40's - After his return from Sicily, I think it's worth saying Vito Genovese gained broader influence than any other head of a family. That being said, he wasn't able to consolidate it for more than a short period of time. Therefore, it's basically null.

50's - 70's. Gambino Family, thanks to the leadership of Don Carlo Gambino and his partnership with Tommy Lucchese

Late 90's - '02. Bonanno Family under Joe Massino. Begins the decline 2 years before Massino turns when high rankers suffer house arrests and minor convictions.

'02 - Present. By staying rooted in generally legitimate business and understanding the value of plea bargains, Genovese reign supreme once again. Probably forever more.