Sept. 26, 1983: The Man Who Saved the World by Doing ... Nothing
What I find most interesting about this event is that there is really no consensus on what would have happened had he believed the alert to be genuine.  When he received an award at the UN in 2006, Russia felt the need to declare that they would not have launched a counterattack without confirmation from other sources.  I think it's a good example of how history is far more subjective that we like to think.
http://en.wikipedia.org/wiki/Stanislav_Petrov