In the book Mortal Error: The Shot That Killed JFK, Bonar Menninger argues that the third shot that hit John F Kennedy was fired by accident by a secret service agent. The book's Wikipedia page summarizes the theory:
Conducting his own investigation, Donahue eventually decided that the bullet that struck Kennedy in the head had in fact been fired by United States Secret Service Special Agent George Warren Hickey Jr. (March 24, 1923 to February 25, 2005) from an AR-15 rifle carried in the car immediately following the President's vehicle.
The series of events is as follows: After the first shot which hit the street was fired, Hickey turns completely around and acquires Oswald on the sixth floor of the school book depository building. His turned head is documented in an AP photograph by James Altgens. Hickey reaches for the AR-15 under the seat, releases the safety and begins to lift the gun. The second shot is fired by Oswald, hitting the president and Texas Governor John Connally.
The president's car and the follow-up car containing Hickey suddenly speed up. This is attested to by Secret Service agent Clint Hill. Agent Hickey, who is unstable because he is standing on the cushion of the seat, rather than the floor of the car, begins to fall back due to the acceleration of the vehicle, pulling the trigger of the AR-15. The gun is pointed toward Kennedy at that instant, and the bullet strikes him squarely in the back of the head.
Was Kennedy shot by his secret service agent?