The last time humanity was almost destroyed was about 80,000 years ago, when a volcanic eruption reduced the human population below 1,000. So say events that can destroy humanity happen on average every hundred thousand years (conservative assumption, right?).
The estimates there range from 2,000 to 20,000 individuals.
The population may not have been significantly bigger before the eruption:
Scientists from the University of Utah in Salt Lake City in the U.S. have calculated that 1.2 million years ago, at a time when our ancestors were spreading through Africa, Europe and Asia, there were probably only around 18,500 individuals capable of breeding (and no more than 26,000).
This seems in conflict with http://en.wikipedia.org/wiki/Toba_catastrophe_theory
The estimates there range from 2,000 to 20,000 individuals.
The population may not have been significantly bigger before the eruption:
http://www.physorg.com/news183278038.html
A volcanic eruption is obviously much less likely to threaten humanity’s existence today than when there were only a handful of us in the first place.