When I was taking ecology in school in 2000, the thinking at the time was that the carrying capacity on this planet for human beings was eight billion. Bad, bad things can happen to populations of organisms when they hit their carrying capacity. Wonder what the current thinking is on this topic (in terms of what our species's carrying capacity is.
Based on how much food/water/energy is wasted every day, and the disparate standards of living, I'd say that the possible capacity is greater than 8 billion.
The notion of carrying capacity relies on either the absolute capacity of the environment (i.e. humans are doing everything they can to maximize their population), or the more realistic theory that knows our current systems and infrastructure fall well short of the theoretical carrying capacity.
Technology is/has rapidly been increasing the carrying capacity for humans, who knows what happens if it slows down while population ratchets up.
Population correction on a massive scale. This is based on the theory that there will be a delay between when the resource pool required to keep the human race growing is maximized and when the population actually stops growing. The length of that delay will determine the size of the correction. This has been observed in many animal species, and its assumed the human race may see something similar happen.
One possibility is that population will fluctuate right around the carrying capacity. War and localized starvation, though not happy topics by any means, can be examples of that kind of possibility. The far scarier scenario is a population crash (manifested in global famines, plagues/pestilence/epidemic, nuclear holocaust, etc.). Definitely a possibility if our ability to match resources and the distribution thereof to population growth becomes insufficient.