Historians have a short list of "close calls" and "war scares" for conflict between the USA and the USSR. The "standard list" includes:

• The Berlin Crisis of 1948

• The Berlin Crisis of 1961

• The Cuban Missile Crisis of 1962

• The War Scare of 1983

One can add or remove other mishaps or tense moments (e.g. the Soviet invasion of Afghanistan), to be sure. Of the above, the Cuban Missile Crisis and the War Scare of 1983 are usually regarded as the closest to nuclear attack. Solkolsi and Tetrais' "Nuclear security crises: what does history teach?" is a nice overview of the many nuclear "close calls," and Hoffman's The Dead Hand is really excellent on the 1980s crises.

Separately, I always think it is important to note that the Cold War was not so cold in the end. It avoided nuclear exchange and direct battle between the USA and USSR, to be sure. But there were dozens and dozens of proxy wars, assassinations, regime changes, invasions, and so on in many other countries. It is hard to look at the Korean War, the Vietnam War, the Soviet-Afghan War, the US overthrowing of governments in South America, the Bay of Pigs Invasion, the Communist revolutions and civil wars in China, Laos, Cambodia, various African states, the ongoing crises in the middle east, the CIA involvement in instating the Shah of Iran and his eventual overthrow, and so on and say "it stayed cold" or wasn't an "actual war." Literally millions died in proxy wars during the Cold War. Yes, it would have been hundreds of millions (at least) if it had gone nuclear. But millions are millions in my book, and I think focusing on the US-Soviet dimension can overlook that. So yes, it was a Cold War, but no, it wasn't actually all that cold.