I don't think it will happen. In mathematics (specifically, statistics), there's something of a saying: the best indicator of the future is the past. Look at the past few million years. There has been one event catastrophic enough to cause mass extinction of species, and that was the asteroid collision that wiped out the dinosaurs. And life still persisted. The likelihood of something like that happening even in the next thousand years is next to zero if we use the past as a yardstick.
That, of course, only accounts for natural disasters. The remainder, then, is man-made disasters. Nuclear war, global warming, etc. However, for every idiot who wants to blow up the world, you've got a few hundred people actively working against them. While I might not like the US government for a lot of things, I can certainly trust them (and other world governments) to work against any force stupid enough to try to endanger everyone. They are, after all, self-serving, and what endangers all of us will obviously endanger them as well. As for something like global warming, same thing. We've got enough people with the power to do pretty much anything they want that if they (or their profits) were in danger from something like that, they'd commit the necessary resources to those of us smart enough to come up with a decent solution.
Our system is not ideal; far from it. But it's sufficient to respond to whatever sort of thing we might try to do to ourselves.
