The FBI spied on Martin Luther King Jr. in an unsuccessful effort to prove he had ties to Communist organizations. In 1963, Attorney General Robert Kennedy granted an FBI request to surreptitiously record King and his associates by tapping their phones and placing hidden microphones in their homes, hotel rooms and offices. A 1977 court order sealed transcripts of the surveillance tapes for 50 years.
http://www.smithsonianmag.com/40th-anniversary/nine-historic...
...some people think he made extensive use of prostitutes, but I expect the FBI would have pulled an "Eliot Spitzer" on him had that been the case. Still, there's something there or they wouldn't be covering it up to protect his saintly image.