Containment was not successful in a number of individual cases, but it was successful overall as a strategy.
During this time, there were places where communism was able to spread. Notably, it spread to Cuba in 1959 and to Vietnam, where North Vietnam became an independent communist country in 1954 and all of Vietnam became communist in 1975. These were clearly failures on the part of containment because it did not prevent communism from spreading.
However, the whole point of containment was to prevent the communists from defeating the US and its allies. Containment was meant to ensure that there would still be a "free world." In this sense, containment was very successful. None of the parts of the world that were most important to the US became communist. By 1985, communism was becoming weaker and would fall within the next 5 years. This shows that, overall, containment was successful during these years.