Answer:
There are many conspiracy theories involving John F. Kennedy's death. Many of them involve the Bay of Pigs and the CIA. Here are three theories to satisfy your question.
1. The CIA Killed Kennedy.
After the utter failure of the Bay of Pigs, President Kennedy lost faith in the CIA. He mostly ignored their suggestions, as seen in the Cuban missile crisis. Many at the CIA feared they would lose their job. When the Cuban Missle Crisis arose, many members of the military urged Kennedy to prepare for war. He didn't. He peacefully dealt with the situation. Thus, hurt feelings and angered members lead to his assassination. It is important to note and a proven fact that the CIA had hired the mafia to murder the Cuban leader, Fidel Castro.
2. Lyndon. B. Johnson Killed Kennedy.
If Kennedy won the next election, he planned to replace Johnson. Thus, people believe Johnson ordered Kennedy's death.
3. Revenge!
After the Bay of Pigs fiasco, Fidel Castro wanted revenge on Kennedy. Thus, he ordered Kennedy's death. A similar theory holds that Russia hired the assassin, who was a communist, to kill Kennedy.
Please remember these are simply theories. Aside from the first one, all of them have been proven false. Have a great one!