Bay of Pigs
Cubans looking to reclaim their island home

In January of 1959, Cuban nationalist Fidel Castro and his band of revolutionaries overthrew General Fulgencio Batista who the US backed to take over the country some seven years before. It wasn't so obvious at the time but it turned out to be a communist revolution as Castro nationalized many US owned businesses, from agriculture to oil refineries to Havana's night clubs and casinos – some owned by mobsters like Santo Trafficante.
As usual, Allen Dulles used the CIA to look out for American interests in the nearby neighbor and President Eisenhower was not happy with a communist regime ninety miles off our shore. Dulles to do something about the situation.
He worked with Cuban exiles who were already looking for a way to get their country back. They were equipped, trained and financed in large part by the CIA. It was generally thought that Richard Nixon would win the 1960 election and continue the plans that were developing.

When the election went to John Kennedy the plans were still moving forward. When he learned of them, he told Dulles they could go forward, but that there could be no appearance of US involvement. What the CIA director did not know was that Kennedy had been communicating with Castro through back channels for some time and was looking to establish some kind of mutually beneficial relationship.
There were a few changes in the plan to make it look less like it was an American operation, but as was Dulles usual disregard for presidential directives Cubans began bombing Castro's air fields with US supplied B-26s and on April 17, 1961 – only a few months into the new administration, the full scale invasion by exiles began.
The met with initial success but as they proceeded inland they got bogged down and need US air support. Dulles believed that once the assault was underway, the president would have to give his approval for the planes warming up on a nearby aircraft carrier to join the attack. Kennedy refused to have American planes attacking Cuba. He did not like being put into a position where he could be forced to do something contrary to the kind of deal he was negotiating... and he fired Allen Dulles and Bay of Pigs organizer Charles Cabell.
There were many repercussions from this fiasco. Primary among them it caused Castro to look to the Soviet Union for assistance. This assistance eventually took the form of Soviet missiles just 90 miles from the US which was another can of worms for the young president. They were removed after a few tense weeks, but part of the agreement was that the US would leave Cuba alone and not try to depose the bearded dictator.
This agreement did not seem to bother those preparing for another invasion – which never took place.
Bay of Pigs Declassified: The Secret CIA Report on the Invasion of Cuba
by Peter Kornbluh
For decades, the CIA's top secret postmortem on the April 1961 Bay of Pigs invasion has been the holy grail of historians, students, and survivors of the failed invasion of Cuba. But the scathing internal report on the worst foreign policy debacle of the Kennedy administration, written by the CIA's then–inspector general Lyman Kirkpatrick, has remained tightly guarded―until now.Dislodged from the government through the Freedom of Information Act, here is an uncompromising look at high officials' arrogance, ignorance, and incompetence, as displayed in their attitude toward Castro's revolution and toward the Cuban exiles the CIA had organized to invade the island.
And too many more go list here... check them out.