Bobby Kennedy and Richard Nixon both apparently believed that LBJ had Kennedy killed. Similarly, E. Howard Hunt, the former CIA agent and Watergate burglar, made a deathbed confession to his son that LBJ was at the center of a plot that relied on CIA officers and mob types, with Hunt having a peripheral role.
Notably, the two major official investigations -- the Warren Commission and the House Select Committee on Assassinations -- came to differing conclusions, with the later House Committee finding that Kennedy was killed by a conspiracy set up by Mafia bosses Carlos Marcello and Santo Trafficante.
Two bits of information that I learned through personal friendships also incline me to think that there was a conspiracy.
Although publicly denied by the CIA, I know for a fact that CIA officer David Atlee Phillips used the cover name "Maurice Bishop." That being so, there is reason to credit a witness who swore to the House Committee that he saw Phillips using that cover name and meeting with Oswald before the assassination.
Also, among at least some of Santo Trafficante's family relations who were not involved in organized crime, it was believed that he had something to do with the killing of Kennedy. As my source explained, when, in his early twenties, he flatly asked his parents if the rumors about "Uncle Santo" being involved were true, he was told yes, but to never ask about it again, and that among his wider family, to never refer to JFK or the Kennedys and to especially never mention Dallas.
Even if Oswald fired the shots which killed Kennedy, the fact that Oswald was killed two days later strongly suggests that there was a conspiracy--the other members of which had to make sure Oswald was silenced.
Oswald made a big show of defecting to the USSR and later of passing out pro-Castro literature...but was he really a Communist or was that an act?