The Aliens Theory
Technically the CIA's behind this one, too, but it's way weirder. Basically, the theory says that JFK requested some top-secret intel on UFOs 10 days before his death. The CIA just couldn't let him have it, so they decided to bump him off instead.
The strongest case for: Author William Lester claims that, in response to a Freedom of Information Act request, the CIA released Kennedy's actual letter. Lester published the whole thing.
The strongest case against: Historians have doubts about the authenticity of that letter, and the actual evidence of CIA malfeasance rests on a "burned memo" UFO hunter Timothy Cooper claims he received from a CIA employee. In it, the director of the CIA says, "As you must know, Lancer [JFK's codename] has made some inquiries regarding our activities, which we cannot allow." That's pretty shady stuff, only the memo has never been verified. And UFO hunters fall somewhere between "Stephen Glass" and "cash-strapped Nigerian princes" on the credibility scale.