You guys really think humanity will completely die out from even global war? I think that no matter how many bombs go off, there will be people who are in safe areas. The radiation could be a worldwide problem, but I find it hard to think that would kill off everybody.
And if there is survivors, I have a feeling they would survive and the world would very slowly repopulate with humans. Albeit it would be a much different culture and technique of living.
I think a pandemic is much more likely to destroy society anyways... Or a solar storm.