The United States, always a Capitalist country, has maintained an intensively anti-Communist policy. This applied not just to the USSR, but to Cuba eventually as well.
Before the Cuban Revolution, the United States had controlled much of the Cuban economy. After the Spanish-American War, American companies were able to buy huge amounts of land in Cuba, and held considerable influence over the Cuban government and society.
U.S. businesses made large amounts of money off of Cuba through sugar mills and other businesses. The American Mafia also exploited Cuba and made vast sums of money through illegitimate means.
After the Revolution, the United States was immediately suspicious of Cuba. When Fidel Castro visited the U.S., Richard Nixon developed the opinion that he was being controlled by Communists.
An Agrarian Reform Law displeased the U.S., though the United Nations praised it as "an example to follow." Many American companies lost land, and didn't accept the government bonds offered to them in return for their property.
Eventually, the United States decided it wanted to replace Castro. The CIA was put in charge of launching an attack on Cuba using anti-Castro exiles. Within three days, the attack was fully defeated and the U.S. humiliated.
A year later, the Soviet Union deployed missiles to Cuba. Though he thought they added little to Soviet power, President Kennedy felt the issue was good politics and made a big deal of it. With an American invasion on Cuba coming and U.S. nuclear bombers in Soviet airspace, Khrushchev gave in and the U.S. got its victory.
After that, the CIA for many years tried to kill Castro and destroy the Cuban government. In Operation Mongoose, the CIA devised many schemes to kill Fidel, but none succeeded. The CIA also ruined Cuban crops, destroyed factories, and in other ways sabotaged Cuban economic production.
The U.S. government has also taken a friendly stance towards anti-Castro exile groups, despite the fact that many of these groups have carried out terroristic actions. In 1992, President Bush pardoned Orlando Bosch, who was suspected of killing 73 people in a Cuban airline bombing, but fled from jail.
The U.S. attitude towards Cuba has not changed much. All American presidents have insured the public Castro will fall, but he has outlived them all.
Today, the anti-Cuba policy stands little chance of changing due to the political power of anti-Castro exile groups.
The U.S. continues to oppose Castro, but in less violent ways, for instance by supporting right-wing, capitalist propaganda broadcasts to Cuba via Radio Martí and TV Martí. The U.S. also maintains its blockade, which it will continue to do until Cuba adopts the American economic system.