A lot! For one, during the colonial period and the American Revolution, there were plenty of conspiracy theories that the British and/or the French (depending on who you talked to) were secretly infiltrating American politics and perverting events. But probably the most commonly held conspiracy theory that has more or less (but not entirely) fallen by the wayside is the fear of Catholics... This was widespread by American Protestants, who felt that Catholics were taking orders directly from the Pope or their priests and that they were infiltrating American culture with an eye towards domination. This persisted well into the twentieth century (JFK had to give a speech saying he wouldn't listen to the Pope if elected president!), though within the last 50 years Protestants on the American right have aligned with Catholics over social issues (abortion, school prayer, etc.) and have largely abandoned that conspiracy theory. (This is something I follow a great deal in my forthcoming book, Under the Eye of Power, that follows the history of American conspiracy theories surrounding secret societies.)