Oswald might have done it.
Oswald pulled the trigger but other people or at least somebody probably knew when it was going to happen and said nothing about it which makes it a conspiracy of sorts.
Of all of the wild conspiracy theories, the only one that sounds half right plausible and make sense from a who would benefit greatly from it is that LBJ did it – He was a ruthless and extremely ambitious character according to all that knew him. He lusted for power unmatched by few in his day and he was corrupt through and through. In October of 1963 a Senate Committee that was investigating LBJ ‘s protege Bobby Baker for corruption had turned their attention to the Vice President and his shady dealings. There was rumors in the media that Bobby Kennedy wanted JFK to dump LBJ off the ticket. Reportedly JFK said no but LBJ still felt embarrassed and was greatly concerned about the investigations they could literally send him to jail, in fact on the day of the assassination, some reporters were gathering in NY to discuss what they gathered about Johnson. He was boxed in with no real power that he desperately wanted and knew he couldn’t get as a Vice President. He was standing behind a young fellow and his brother who didn’t care much for him and now investigators were turning up stuff about him. That must gave him the feeling that his goose was cooked, especially if they lost the election of 1964 (the reason they were in TX was to sure up waning support). He had to get JFK in TX where he and his cronies had controlled the state and powers that be.