catastrophe

If the present rate of technological advance continues, we can expect a major human induced epidemic within the next 50 years, directly killing, lets say, 30% of the world population. The indirect lethality rate---from a massive economic collapse accompanying the epidemic---would likely make things much worse.  This will probably happen sooner if reports are correct about the Soviet Union having weaponized a particularly lethal strain of small pox. Within 100 years, it is plausible nuclear technology will be so advanced that the destruction of cities by nuclear weapons will be a commonly occurring nuisance, and within 200 years, it will be fairly easy to manufacture weapons capable of destroying the entire planet.

Of course, any near term catastrophe will have a substantial effect on the pace of technology, so the rest of the story could take longer to pan out.  Also, on a positive note, the creation of technology capable of destroying the planet will most likely be accompanied by a technology that makes energy production basically free, making space colonization far easier to accomplish.