Here is my theory and you did not put it in your poll.
We tried to kill Castro. He retaliated by assisting in an elaborate plan to kill Kennedy. I think Castro owned the plan overall.
Castro contracted with the mob for Ruby to kill Oswald to silence him. The Russians supplied Oswald and a backup shooter.
So the answer is, Castro, the mob and the Russians. I think various US law enforcement agencies covered up all these connections to hide our vulnerabilities and avoid embarrassment. So you could say our government was involved, at least as far as covering up what really happened.
Another thing to think about. Ask yourself why we have not normalized relations with Cuba. Cuba has long past being a threat to the US. My answer is because Fidel is still alive and we will not normalize relations with Cuba as long as he is alive. Watch. The minute Fidel dies, and maybe Raul too, we will normalize relations with Cuba.
Now, where did I put my tin foil hat?
References -
#1 Castro - The Church Committee stated that it substantiated eight attempts by the CIA to assassinate Fidel Castro in 1960-1965.[2]:71 Fabian Escalante, a retired chief of Cuba's counterintelligence, who has been tasked with protecting Fidel Castro, estimated the number of assassination schemes or actual attempts by the Central Intelligence Agency to be 638.[3] Some of them were a part of the covert CIA program dubbed Operation Mongoose aimed at toppling the Cuban government. The assassination attempts reportedly included cigars poisoned with botulinum toxin, a tubercle bacilli infected scuba-diving suit along with a booby-trapped conch placed on the sea bottom, an exploding cigar, a ballpoint pen containing a hypodermic syringe preloaded with the lethal concoction Blackleaf 40, and plain, mafia-style execution endeavors, among others. There were plans to blow up Castro during his visit to Ernest Hemingway's museum in Cuba.
http://en.wikipedia.org/wiki/Assassinat ... del_Castro
#2 Ruby - In 1963, Sam and Joe Campisi were leading figures in the Dallas underworld. Jack knew the Campisis and had been seen with them on many occasions. The Campisis were lieutenants of Carlos Marcello, the Mafia boss who had reportedly talked of killing the President.
http://en.wikipedia.org/wiki/Jack_Ruby