One of the little told stories of the Yom Kippur War, known also as the Ramadan War and the October War, which took place between Israel and a coalition of Arab nations was the potential that it could have escalated into a third world war.
The New World Encyclopedia article on the war, which took place in October, 1973, mentioned that the flashpoint occurred when Israel had turned the tables on the Arabs, defeating and pushing back Syria on the Golan front and surrounding one Egyptian Army on the Suez front and cutting off another from supplies by mounting a counter offensive that saw Israel forces on the Africa side of the Suez Canal. Israeli forces were, at one point, 101 kilometers from Cairo.
The United Nations had passed Resolution 338 calling for a ceasefire on October 22, 1973. However the Egyptians broke the ceasefire, resulting in an Israeli push that completed the investment of the Egyptian Third Army, trapped on the east bank of the Suez Canal.
While Secretary of State Henry Kissinger was negotiating a restoration of the ceasefire, including the shipment of non military supplies to the trapped Egyptians, Soviet leader Leonid Brezhnev sent American President Richard Nixon a letter that, in effect, threatened Soviet military intervention in the conflict. Seven airborne divisions were moved into position along with Red Air Force units and amphibious transports with 40,000 naval infantry, the Soviet version of Marines.
In response the United States government placed American forces on Def Com 3 and sent Egyptian President Anwar Sadat a message to demand that he withdraw any request for Soviet military intervention, promising that the United States would respond in kind. The Soviets, concluding that a military conflict with the United States in the Middle East would be catastrophic, backed off. The United Nations passed a new resolution imposing a cease fire and this time it held, with fighting for the most part ending on October 26, 1973.
The Global Post notes that while the war was going on, the United States Sixth Fleet and the Soviet Mediterranean was eye ball to eye ball, in effect, with a naval conflict possible at any moment. The Soviets had more ships and a doctrine that suggested a first strike. But the Americans had aircraft carriers and thus almost certainly have prevailed in any battle in the Eastern Mediterranean.
Of course this was the scenario that kept a lot of military planners up at night during the Cold War, a hair trigger conflict with every potential for getting out of control and resulting in nuclear tipped ICBMs flying. Fortunately the Middle East crisis did not escalate into such a catastrophe.