200 to 300 years out there is no humanity as we know it today. Whatever we are at that juncture, it won't be "human" as we now define it. Our self directed evolution has long since taken over, and it's accelerating at an extraordinary clip. You can debate the merits of that, the details of it, but it's happening either way.
In the next two or three decades we'll have begun to completely take over genetic alteration / evolution / improvement / etc, of our species. Within a few decades after that, we'll be severely altering what we are. Within 150 or 200 years, it'll be very hard for modern humans to relate to the ancestor humans from 2012.
Concerns about asteroids or global warming and so on are moot. We won't be here as a species pumping CO2 into the atmosphere or waiting around helplessly for a rock to crash into the surface. It's not an issue of if, it's just an issue of how long it takes and how many competing models of our self directed evolution become options.
The sole threat to that future is super virus / disease, most likely man-made. It's the only thing that could stop our evolution and wipe out our species in that couple hundred year time frame. Even nuclear war isn't a threat to species survival, you could detonate thousands of nukes simultaneously and it wouldn't come close to killing us off.