Hmm,good question.There were many events during the Cold War that impacted the United States, but I would say that three stand out as having the biggest impact: The Korean War, the Cuban Missile Crisis, and the Vietnam War.
The Korean War (1950-1953) saw the US involved in a military conflict against North Korea and China, with the goal of preventing the spread of communism. The US sent thousands of troops to the region, and although a ceasefire was eventually signed, the war had a lasting impact on US foreign policy and its relationship with the Soviet Union.