As two significant Cold War events we can take the wars in Vietnam and Afghanistan.
The war in Vietnam was a war in which the US got itself involved because it didn't wanted to allow the communist to take over Vietnam, a strategically very important country, and be an ally of the Soviets. It was a long and bloody war, with hundreds of thousands dead and injured. The consequences of this war were that the US got its reputation shaken because of the loss, but also a long term negative effects on the population of Vietnam because of the usage of toxic and radioactive substances.
The war in Afghanistan was waged between the USSR and the US supported Afghanistan. The Soviets wanted to occupy Afghanistan and set up a communist government, which of course the US didn't wanted. After the initial success of the Soviets, the Afghans managed to push them away. The consequences were that the Islamist took over the country, and the weapons provided by the US was left in the arms of extremist Islamic organizations, which eventually led to the formation of terrorist organizations.
