The Cuban Missile Crisis is one of two times that the US was at DEFCON 2, which is the second highest readiness of the military. At DEFCON 2 armed forces ready to deploy and engage in less than six hours, with the readiness of the next step to nuclear war. As it turns out we were even closer to that than originally thought.
(Quick aside, DEFCON 2 is the highest level of readiness the US has ever been at, never reached DEFCON 1. DEFCON 1 is when they know nuclear war is imminent or has already started)
Soviet Submarine B-59 was in the Caribbean to support Soviet arms deliveries to Cuba. However on October 27, a US task force that included 11 destroyers detected it. They dropped very low-yield training depth charges to try and force the submarine to the surface for positive identification, as there was no way to get in contact with it. B-59 had not been in radio contact with Moscow for several days, and was too deep to hear any radio traffic so they were confused if they were really being attacked or if they were at war or not. The Captain wanted to retaliate with a T-5 Nuclear Torpedo.
The three senior officers had to unanimously agree to launch the nuke. Captain Valentin Savitsky and Political Commissar Ivan Maslennikov said yes, but this was vetoed by the Executive Officer, Vasili Arkhipov. Arkhipov eventually convinced the Captain to Surface and await clear orders from Moscow. The sub needed to surface anyway, as their batteries were running dangerously low and the air conditioning had failed. B-59 surfaced and set a course back to the Soviet Union.
TL;DR: One man managed to prevent all-out nuclear war at the height of the Cuban Missile Crisis.
en.wikipedia.org
