Personally, I think a natural diaster is far more likely to cause the destruction of the human race rather than a nuclear war. Nuclear weapons are great bargaining tools, which countries use to win political leverage - it's highly unlikely they'll actually be used aggressively.
I think there are three natural problems which could destroy the human race. They are:
- Asteroid impact. This is the most obvious one, but one which poses a real threat. It's happened before, and it will happen again, it's merely a question of 'when' rather than 'if'. Having said that, asteroid strikes are very rare in the history of our planet.
- Global warming. Due to man-made pollution and natural processes our earth is becoming less able to sustain life. If the Ozone layer contains to be destroyed, and the temperature of the planet continues to rise, we could find ourselves in a no-way back situation. The worst thing is, some of the world's most polluting countries are too ignorant or greedy to try to reduce emissions.
- Disease. I believe that a pandemic disease is the greatest risk to the survival of the human race. The heavy prescription of anti-biotics in the late 20th century has meant that certain diseases have mutated to become immune to this treatment. Diaster would occur if a new deadly disease spread and there was no cure - much like the plague in medieval Europe. Globalisation will mean that anything like this would easily be spread to all corners of the globe.
The world is a far more unstable place now than it ever was during the cold war. Back then, mutually assured destruction (MAD) meant that no side would be stupid enough to launch a nuclear attack, because they would be wiped out by a retaliatory strike. Hence why the cold war was one of the most peaceful times in European history.
We now live in a world which is no longer West Vs East, instead there are a multitude of different national, cultural and religious factors that could start nuclear war. This new world is certainly more unstable, but I don't think it would make nuclear war a likely prospect.