The good news is that on large, people don't want to die, and everyone knows that the odds of that are high if you decide to start a nuclear war.

The most likely incident would be caused by a technical failure. An alarm system that gives a false positive, or a bomb that is accidently released. Similar situations have already happened in the past and often its just been a few well grounded individuals that have made the right decision.

Terrorism is another big one. If a weapon gets in the wrong hands, I'm sure anyone willing to kill themselves won't blink at detonating a nuke.

Nuclear war is always the immediate worry that might happen. Global warming is the longer term worry that will definitely happen..and might lead to nuclear war.