My view is that the decade that had the greatest impact on the world in this time period was the decade of the 1960s.  I say this because that decade saw the Vietnam War, the counterculture, and the Civil Rights Movement in the United States.  All of these events had a great impact on the US and on the world as a whole.

The Vietnam War changed the way in which the US conducted its foreign policy.  It made the US much less aggressive and assertive for many years.  It also led to the establishment of diplomatic relations between the US and China, which helped lead to the subsequent rise of China.

The counterculture and the Civil Rights Movement had impacts around the world as well.  The Civil Rights Movement occurred at more or less the same time that African countries gained independence.  These events helped promote the idea of minority rights around the world.  The counterculture and the “sexual revolution” changed social values throughout the Western world.

For these reasons, I would argue that the 1960s were the most important decade in the last half of the 20th century.