DC, I would like to respond to your question with a broad interpretation of "influential"--because "influential" could mean positive or negative influence.
Al Capone was undoubtedly the most influential in a negative sense. He was so prominent, so outrageous, so bold in his flaunting of his criminal enterprise and wealth that his name is forever synonymous with organized crime. And, unfortunately, he tarred generations of Italian-Americans with the "Mafia" brush, even though the Mafia never had more than 5,000 made members (out of more than 25 million Italian-Americans), and even though Capone himself wasn't in the Mafia. Toto Riina, through his murderous excesses, almost singlehandedly mobilized Sicily against the Mafia, after centuries of power.
On the positive side, Don Vito Cascio Ferro is most responsible for the genesis of the five New York Families, and for setting up a Europe/Middle East/American narcotics pipeline. And, as posted before, Charlie Luciano's formation of the Commission pushed the Mafia into becoming a nationwide cartel. I'd say he was the most influential American Mafioso.
Meyer Lansky, as an individual, achieved more influence than any other organized crime figure acting as an individual--that is, without an organization and muscle backing him. Lansky for decades counseled nearly all the major Mafia Dons. His advice made the Mafia predominant in gambling--particularly legalized gambling in Cuba, Nevada and the West Indies.