I think Benjamin Franklin is the quintessential American. He was an inventor, a statesman, a writer, very concerned with industry and how to live a moral life. His rags-to-riches story is still echoed in other iterations and reincarnations of the American dream that says this is the land of opportunity filled with people willing to make their own destiny. To be American means adapting to survive and putting aside the inheritance of European fatalism, and that’s the way I see Franklin. The face of our highest denomination of currency, he’s the symbol of American enterprise, capitalism, and greed. Even though he probably wouldn’t even call himself an American, he was part of the nation’s creation and stands at the intersection of the young Republic and its rich colonial history that was so valuable in defining American culture.
This is a tough question to answer for the US. I think there are so many defining characteristics that we have (compared to other nations, especially from the outside looking in), and it’s tempting to point to Franklin as the American icon because he fits so many of these Americanisms. Of course that neglects our unparalleled diversity in favor of a dead white man, but I can’t think of a better single person to call our “greatest cultural icon.”