How many times has the world been said to be "close" to nuclear war?

World leaders are not insane but aware of the risk. The idea to wage a war is to win - and you are not likely to win if your own country is dragged into a nuclear disaster. Put bluntly, the knowledge of being threatened yourself would more than likely keep you at bay. Most of these threats are cooled-off with diplomatic negotiations which all boils down to how much is it going to cost. More than once has North Korea threatened serious conflict but rarely do you see real action. It can be serious of course, but it is not unusual that wealthier nations tend to pay-off with concessions with the guarantee that the situation will change to benefit both sides. At one stage a massive shipment of food supply was sent to please the north Koreans all under the aegis of good will of course. They had done the same with Israel whom had threatened the Arabs that if they did not stop firing the scud missiles into their territory they would use nuclear missiles to take care of them. The negotiations were such that the Israel's were promised 4 billion dollars over three years to smooth things over as long as they avoided pressing the button.

Just a few times, and you're aware of the worst time, the Cuban Missile Crisis. Do note, however, that there's nuclear war, a nuclear "exchange", and a use of a nuclear weapon. While a full nuclear war could kill off most life on the planet, the second or third would still be horrible events. I'm an old man, and will hopefully not live long enough to see it happen, but I believe we are now closer than ever to that horror. Too many players, some of whom are not particularly stabile or predictable. For a plausible movie, try "The Sum of All Fears".

In terms of an intentional launch as a matter of informed policy, the closest the world has probably gotten was the Cuban Missile Crisis of 1962. The Soviet Union had placed nuclear missiles in Cuba, which had recently become Communist. These missiles were close enough that Americans would only have a few minute warning before they hit. The US demanded their removal and blockaded Cuba. The Soviet Union ultimately agreed to remove the missiles but the situation could have escalated to nuclear war.

There have been a couple of times where there were false alarms on one side or the other which caused a brief stir but weren;t acted upon. For example, there was one point where the military called the White House during Jimmy Carter's presidency saying that the Soviet Union had launched their missiles. But before the president could be found and informed they called back saying that it had been a false alarm.

You appear to already know about Cuba in 1962, other incidents which brought the world cliose to WW3 include the following:-

In 1967, a Soviet submarine armed with primed with nuclear missiles came to within 100 miles of Hawaii, but luckily sunk due to a conventional explosion on board before they could be launched.

In 1983, a Japanese civilian aircraft strayed into Soviet airspace and was shot down killing all passengers crew, this brought the world close to war. The Soviets always insist that the US was using it as as spyplane, even though the Japanese would have been unlikely to allow the US to use a full civilian aircraft for spying missions, but no explanation was ever given for as to why the airline had gone so far off course.

In my childhood in the early 60s, it would be during the Cuban Missile Crisis. When giving out his 7-step program in response to the discovery of Soviet IRBMs being assembled in Cuba, the third point was that "It shall be the policy of the United States to regard any missile launched from Cuba to any target in the Western Hemisphere as an attack by the Soviet Union on the United State, requiring a full retaliatory response." Thanx.

That depends on how you define "close". DEFCON 2 is the next step to nuclear war, and we've only been at DEFCON 2 twice. DEFCON 3 is an increased level or readiness, and we've been there three times.

The Bay of Pigs event almost had us there.

No one is going to nuke. Only the media talks about that and they don't know ****