Okay: I didn't vote in the "Sports" category because I don't know enough about the history of American sport.

As far as actors go, the first three that come to mind are:

Lon Chaney - a precursor to method actors such as Brando and De Niro, fully transformed himself in the role and made some brilliant characters with unforgettable performances.
Marlon Brando - naturalism defined, both cinematically and theatrically; only Klaus Kinski has the same presence when keeping his mouth shut.
Charlie Chaplin - though English, he is the face of American cinema (and therefore popular American society): significantly, tellingly and ironically, he became a blacklisted scapegoat, along with many others, under McCarthyism. Shame on a nation, really.
(honourable mention to Lillian Gish for sheer acting excellence, John Wayne for cultural significance and Humphrey Bogart for embodying, for me, 1940s Hollywood)

As far as entertainers go:

Elvis - undeniably the most significant "entertainer" to come from the States; he didn't write his own songs and he could barely act, but what stage presence and fandom.
The Beatles - again, an English import, but their popularity in the US is significant indeed; prolific, popular and very hip; they've never gone out of fashion, really. Lennon's murder was fortuitous in light of his Jesus-like legend.
Bob Dylan - the greatest songwriter ever, in my opinion, and after Eliot and Pound (chronologically, not qualitatively), probably the greatest poet of the 20th Century period. Enough said: I could write pages and pages on him.