The Cuban Missile Crisis, both superpowers were not only very close to destroying each other but they also had access to a nuclear missile that's close to their respective enemies. 
Able Archer for me I think.
Interestingly the KGB believed that lights being on in the MoD in London late into the night was evidence that NATO was planning an attack. However in reality it was just to allow the cleaners to do their job.
That particular crisis illustrated that the KGB was excellent at gathering information, but terrible at analysing what it actually meant.
Your favourite Cold war close call?
We have favourites, now? Jesus, has it been that long that the Cold War's been over?
Yes, old man!p)
I remember when we used to be scared of the Russians. We even had a President who signed a bill outlawing Russia forever...the bombing was supposed to begin in five minutes...
...and while I'm reminsicing, get off my lawn!![]()