This is the source of the intense push to extremism and denial of much more minor, yet more likely, events. I strongly suspect Cuba was involved in the whole JFK thing. Now to discredit my view you'll get screaming nutjob conformist extremists claiming "I" must think cuban special forces paratrooper sniper army teams blew away JFK and ridiculous stuff like that in order to enforce conformity.
What I actually personally think is he was a nutcase and most likely went to the Cuban embassy and told some minor functionary his plan and asked for cash or help, at which time the Cuban embassy functionary, if he wasn't a total idiot, told him he's nuts and get the heck out, they're not going to help start WW3. Maybe the Cubans even told the SS but the SS blew them off too (just another nutcase or some triple crossing secret agent BS). Maybe the Cubans even gave him $10 and some bus tickets just to go the heck away. But after it actually happened, the whole thing has to be buried or it turns into an icky international incident. So my view is technically Cuba was involved, its just not at the level that extremists on either side claim in order to poison the well and prevent any further discussion. Or maybe the local police chief who laughed at him instead of reporting him was "involved". Or some SS agent who thought Oswald was a joke was "involved".
My point is there was a coverup of bad (sorta) judgment not an elaborate conspiracy / coup. Only sorta bad in that you can't assume every nut will actually do something, that would be a massive denial of service vector, handy to implement if you were actually planning something real...
I suspect that in a century when its all dusty and blown over, someone will release a letter some crackpot wrote to the Cuban ambassador explaining exactly what he planned to do (and did in fact do) and asking for help. Was it good to prevent WW3 in the 60s by covering it up? Yeah probably. Is it still a good idea in 2013? Eh. In 2113 will it matter? Probably not, so we'll finally get the truth.
Its the difference between information and actionable information. So the Cubans knew what was going to happen because he told them, well who cares what matters is what action is taken. In the 60s when the blood was still wet that would have meant WW3. Until Castro dies I guarantee nothing will be released because otherwise people will be asking for his head. In fact I'd give it an extra decade after Castro dies just to make sure theres no possibility of any course of action.
As for a conspiracy, well, it seems to have worked, JFK ended up fairly dead, now if there was a high level conspiracy you can examine history and see what they unleashed, which is pretty much ... nothing. Not even something failed. Other than certain Cuban political leaders getting downgraded from dislike to being more hated than any other human on the planet beyond any public rational level, not much really happened.
If a leader is assassinated in most parts of the world, one of the first things that springs to mind is: coup. If it happens in America, it's assumed to be a nutjob, a "lone gunman." Americans have been extraordinarily naive about their own government, and perhaps critically far too much so in the last four or five decades (in which the US became the sole superpower and all the responsibility that entails).
Even now as our government slaughters civilians with drones, tortures people, threatens allies, tries to start new wars regularly (Syria), spies on every world leader they can get their hands on, abuses every friendly relationship in just about every way possible - Americans still think it's all for the best, to fight "terrorism" or some other horse shit made up excuse.
In a word, Americans don't want to believe their government has become evil. So into the sand the head goes.