JFK was murdered by a Communist who lived in the USSR for years. Seeing how this was during the Cold War, it's very possible the Soviets killed him.

Ever since, the US has become more and more tolerant of Communism. They handed Vietnam to the Viet Cong, they opened trade with China, Marxism started becoming politically mainstream — the only reason we even won the Cold War was because the Soviets destroyed themselves.

I wouldn't take CIA collusion out of the equation — the Soviets very well infiltrated our government — but my main conspiracy is that the Communists killed him.