Cuba (or at least its government) got two major benefits from the Cuban Missile Crisis.
First, Cuba got a guarantee from the United States that the US would not invade the island. This was a concern for Cuba because of the Bay of Pigs attempt in 1961 and because of general US dislike of communism. The US guarantee eased this worry.
Second, Cuba got a closer relationship with the Soviet Union. With Cuba having proved its willingness to support the Soviets, the Soviets continued to provide large amounts of aid to Cuba. This continued until the collapse of the Soviet Union.