The previous answer looks only at whether communism still exists (and it sees China as a communist country, which is a fairly iffy proposition these days). This is not how scholars of international relations would approach this question.
To scholars of international relations, the issue is whether a bipolar international system (one with two competing superpowers) is more stable than a unipolar system (one with only one superpower). In the years after the breakup of the Soviet Union, the international system has been unipolar.
Scholars argue on both sides of this question. Some say a bipolar system was more stable. They would argue, for example, that relatively small regional conflicts like the Iraqi invasion of Kuwait or the current conflicts between Iran and various of its neighbors would not have happened in a bipolar system. The two superpowers would have prevented these things from happening. In this view, a bipolar system was more stable because it reduced the number of potential conflicts.
Others would argue that the current system is more stable because there is no longer competition between two superpowers. We no longer have a situation in which the two superpowers are stirring up trouble around the world, trying to undermine each other's allies (as in the Vietnam War or the US-backed coups in Guatemala and Iran in the 1950s. In this view, an end to superpower competition reduces the amount of conflict worldwide.
There is, then, no clear answer to this question. Instead, different scholars take different sides.
Communism is still prevalent in many countries worldwide and the breakup of the Soviet Union is only a small part of the overall process of obtaining a stable world order.
By definition, Communism is a form of government in which the state controls industry, social programs, and government. Some of these countries prohibit free enterprise; to prohibit the ownership of land and businesses; to dictate a person's occupation or career; to prohibit large families and enforce birth control; to control the press and prohibit free speech; to control the military and require mandatory service from both men and women; to prohibit the possession and use of firearms; to prohibit their citizens from leaving the country and restricting free travel within that country.
According to aneki.com, the five big Communist countries in the world today are Cuba, North Korea, China, Vietnam, and Laos. The biggest threats today are North Korea and China.
The breakup of the Soviet Union has greatly improved conditions in Europe and lessened the world's political strain, but much still needs to be done to achieve world stability.