AFAIK, most research suggests that 1st world countries have low birth rates, in fact most with populations that would naturally decrease (or very very very slowly increase) if not for immigration.
As more countries modernize, they will likely follow this pattern as long as religion doesn't stand in the way.
Earth's population (as I have heard/read, etc.) will probably top out at 9-12 billion sometime in the next 100 years and then slowly begin to shrink.
I believe that it would be beneficial for the human race to focus resources on developing technologies that will allow terraforming of other worlds. To some it sounds like science fiction but it likely can be done at some point in the future and Stephen Hawking is right, if the human race is to avoid being wiped out by a single catastrophic disaster, we need to explore space as much as we can and learn how to colonize other worlds.
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Huge thanks to Dion for the signature!
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