The Korean War ended in a stalemate. When the Korean War began, the border between North and South Korea was the 38th parallel. North Korea was communist, and South Korea was non-communist. At the beginning of the war, North Korea nearly conquered all of South Korea. Due to a daring military action by the United Nations forces, North Korea was forced out of South Korea. South Korean and United Nations forces entered North Korea and nearly won the war. Then the Chinese entered and pushed the South Korean and United Nations forces back to the 38th parallel. The war bogged down here for the next two and a half years. Eventually, a ceasefire was reached. The terms of the ceasefire changed nothing. The border was still the 38th parallel. North Korea was Communist while South Korea was non-communist. Thus, the war was a stalemate with no clear winner.
There are two main reasons for this.
First, the war ended in a stalemate because of Chinese involvement. The Chinese had a huge army that was able to balance out the UN forces and push them back down the peninsula after they had made it as far as the Yalu River which was the border with China.
A second possible reason is that the US did not want to pursue an all-out war against China. Douglas MacArthur, for example, wanted to attack China directly, possibly using nuclear weapons. President Truman, though, did not want to bring on a major war by doing this. The US's desire to keep the war limited in scope is another reason why the war ended in a deadlock.
The Korean war (25 June 1950- 27 July 1953) resulted in a stalemate due to the involvement of a much more power enemy, China.
United Nations forces led by US forces fought for South Korea, while China (and the Soviet Union, indirectly) fought for North Korea. During the war, the North had the upper hand, but an amphibious campaign by UN forces pushed them all the way up to the Yalu River at the border of China. At this point, in October 1950, Chinese forces entered the war and pushed back the UN forces. With the proximity of China, the size of its force and its military might caused a stalemate as UN forces were unable to defeat Chinese forces. A war of attrition continued along with bombing of North Korea. The leader of the UN forces, General Douglas MacArthur, suggested using a nuclear bomb to end the war, however President Truman decided against it.
So a combination of Chinese intervention and Truman's indecisive stance of ending the war led to a stalemate.