John F. Kennedy
Though no one ever called John F. Kennedy a straight-up sex addict, because it was pretty common for men of importance to have numerous mistresses during their terms, the man who got it in with Marilyn Monroe was indeed notorious for all of his physical encounters. Sexual addiction as a problem is actually a fairly new concept; in Kennedy’s time, the early '60s, when he stepped out on his wife he was just cheating.
Cheating a lot, but cheating nonetheless. Kennedy himself did address his own issues, however; it’s said that he once told British now ex-Prime Minister Harold Macmillan, “I wonder how it is for you, Harold? If I don't have a woman for three days, I get terrible headaches.”