How many human beings can be supported sustainably on the Earth? This is a pretty important question for everybody, given that we're all human, all living on the Earth (well, except --OutpostMir--), and our population is increasing so damn rapidly. Look at a graph of world population over time - it's an exponential curve, basically flat at a few million over tens of thousands of years, and then spiking upward alarmingly, so that right now it's damn near asymptotic. How high can that line go before something awful like a Malthusian collapse happens?
Estimates vary wildly, based on the assumptions that go into them. At the low end, Club of Rome, doom and gloom side, we get about an even billion people, who could live at a level of resource consumption near, but not quite at, the level currently enjoyed by Americans. At the high end, estimates go to as much as 25 or 30 billion people, though they'd be living like some '50s nightmare vision of Red China - incredibly poor and incredibly regulated. The basic questions that cause things to vary so much are questions like how much food, power, and processed resources somebody needs to live, and just how much future advances like fusion power and GM crops allow us to push that envelope.
However much we fiddle around with the variables though, one conclusion is inescapable. Something has to change about the way human beings live. Even the best-case estimates, which are probably wildly optimistic, are only a few centuries off at most if the rate of population increase doesn't change radically. Either we implement Zero Population Growth or something damn near close, expand into space in a serious way, or we can prepare ourselves to experience either at the hands of man or nature, what its advocates like to call Rapid Population Reduction. That's RPR for short, and you can go ahead and pronounce that acronym Reaper.