As the other answers states, the United States and the U.S.S.R. only came together because of the severe threat posed by a common enemy, Nazi Germany.

Between 1917 and 1941 relations were tense between the U.S. and the Soviets. Until 1933, the U.S. refused even to recognize the Soviet Union, protesting the Soviet cancelling of its debts to the United States and its nationalization of U.S. property within its border.

After World War II, relations between the U.S. and the U.S.S.R rapidly deteriorated. The United States believed it had behaved honorably to the Soviets, by, for example, holding back its troops from entering Berlin because it had agreed the Russians could take that city. In return, the U.S. felt it was dealt with treacherously. For example, the Soviets had promised free elections in the Eastern European territories it occupied during the war, then manipulated events to install puppet Communist regimes in all of those countries. From the Soviet point of view, the country felt it desperately needed a buffer zone as protection against a predatory West. It argued that it had borne the brunt of casualties in World War II and would not let that happen again.

After the Soviets obtained nuclear capability, more fears arose between the two superpowers, who were ideologically opposed in irreconcilable ways.

The U.S. and the Soviet Union were allies only because they were forced into a very uneasy and uncomfortable alliance. Ideologically they had been polar opposites and it was more chance of fate than anything else that did not put them on opposite sides of the war.

Shortly after the Russian Revolution of 1917, President Woodrow Wilson sent troops to Siberia to aid the "white army" comprised of Russian nationalists in an attempt to overthrow the new Soviet communist regime. This did not endear the U.S. to the Soviets. Prior to U.S. entry in World War II, the Soviets had taken part in an invasion of Poland which Germany had initiated, in fact Germany and the Soviets had secretly agreed to divide Poland between them. It was only when Hitler invaded the Soviets that the U.S. became allied.

Following the war, Stalin commented in a speech from the Kremlin:

The war against fascism has ended; the war against capitalism has begun.

The two never saw things eye to eye, and although they were forced into a convenient alliance, they parted company almost immediately after the war. The Cold War was the logical conclusion which brought both countries to the brink of nuclear war until the Soviet Union finally collapsed.

While it was true that the US and the Soviet Union were allies during World War II, this was only because they had a common enemy: Nazi Germany.  Their systems of government, their economies and their world views were vastly different, and bound to clash.

Once the war was won, these two countries emerged as the only viable empires left on Earth, otherwise known as superpowers.  As the Soviets attempted to spread comunism to new countries, the US adopted a policy of containment, stopping that spread wherever possible.  Since the US already had the atomic bomb, this led to a race for the USSR to obtain it, and a very expensive, very long arms race afterwards.