The Cuban Missile Crisis
This was probably the most tense 13 days of the cold war, in 1962. The U.S. had discovered evidence of Soviet-sanctioned missiles in Cuba, which violated a previous agreement between the two superpowers.
The U.S. decided to react and a tense standoff happened, with plenty of close calls. Finally, JFK and Nikita Khrushchev were able to find some common ground, and the missiles were removed, and Cuba was declared off limits for US citizens.