After reading Barr McClellan's book, I think he's made a very good case that Lyndon Johnson was behind it. Johnson was about to be exposed for the crook he was, and he was able to deflect the investigation into his long list of wrongdoings once Kennedy was gone. Johnson had enough skeletons in his closet and knew enough shady characters to pull something like that off.
P.S.: To those who pooh-pooh the conspiracy theory, over 30 witnesses in Dealey Plaza that day saw the back of the President's head explode with their own eyes. Dr. Peters, the senior attending physician in the emergency room at Parkland Memorial Hospital when Kennedy was brought in, has testified twice before Congress and has said over and over again that he saw the back 20% to 25% of Kennedy's head blasted out. Ask any ballistics expert and they will tell you that the account of a shot from the rear from the rifle of Lee Harvey Oswald killing the President is IMPOSSIBLE. Whoever shot Kennedy in the head was shooting from the front, which means a second gunman and, by definition, a conspiracy.