The war, though long, bloody and costly, also seemed to prove and justify that a policy of containment - stopping the spread of communism to other countries - worked and was justified. This would be part of the reason why we would get involved in Vietnam a short time later. The war was mostly between the US and China, so there were tense relations between our two countries for more than 20 years following the Korean conflict.
It accelerated the Cold War between us and the Soviet Union, as the North relied on Soviet weapons to fight the war, and some Soviet pilots even flew missions against American jets during that time, and we knew it. We accelerated the arms race, and the public became overwhelmingly convinced that the Soviets were bent on world domination, and social hatred of them and communists grew rapidly in the early 1950s.
The major impact of this war was to make the Cold War seem more serious to the US policy makers and to other non-communist countries, especially in Asia.
Because of this war, the US really stepped up its program of containing communism. It increased the number of active duty military personnel in a big way and it started to station more of them at bases around the world.
The US also started to get more serious about trying to help the countries of Asia out economically and militarily. This was when we started to really defend Taiwan and guarantee its security against Mainland China, for example. We also started giving more foreign aid to various countries to keep them on our side.