Supposidly, Bobby Kennedy, when he became Attorney General, wanted to get rid of Hoover and discussed this with his brother, the President. After a face to face meeting between Hoover and Kennedy, that idea faded away immediately.
I suspect the JFK file held by Hoover was probably second in thickness to only MLK, Jr. Hoover had JFK and his daddy figured out in the 30s when Papa Joe was still practicing his "Sieg Heil" salute in front of the bathroom mirror.