The population only grows based on what the environment / technology can currently support. If the environment sucked or technology sucked, then population would be naturally low. If both rocked, then the "ceiling" of population would go up, leaving a lot of potential "empty space" for new people to be born into.
If the population were already at its "ceiling" then for every person born, there would already be another starving - in other words, the population would already have stopped growing.
The only things that can cause mass starvation are things like sudden changes that make the environment suck, or the destruction of technology, or the misuse / idling of productive resources (such as those caused by economic depression or civil war).
For each of those possible "world-ending" scenarios, there are actions we can take:
1) "Protect" or even "improve" the environment, at least with respect to human survival. Things like increasing the amount of arable land, clean water, learning to grow food on the oceans like when we first learned to grow it on land, etc.
2) Improve technology and spread it around (the more people that know it, the harder it is to forget it). Sure the population may be growing, but if it's an educated population, then they'll work together to develop new ways to sustain even more people. Arg! Human beings are a cancer! =) It's more than just human beings taking up a greater percentage of the biomass or increasing the overall amount of biomass, but eventually I see technology as one that will take the elementary building blocks of organic compounds from all kinds of sources, and making organic compounds out of them.
3) Economics and civil wars are obviously highly political issues. If resources are idle or misused because of mere accounting or other reasons and people are starving, then they should just get over their ideology and start using the idle resources. It is the ideology itself that is not fit to survive.
I see concern about "overpopulation" mostly as racism. It seems many just don't want Third Worlders to be "breeding" - well, if they were already starving, the kid who was just born would immediately starve anyway - the fact that populations grow in Third World countries just means the world can support them.
As for those that believe overpopulation is mainly a problem of consumption in wealthy countries, indeed I agree that capitalism is a big part of what makes population growth a threat to human survival: see Demand is not measured in units of people, it is measured in units of money and the discussion of the role consumerism plays in our incentive system.
Indeed we may consume everything and then die out after all resources are gone - but that would be a problem of political and economic policy, which we have full control over. To me, if you wanted less depletion, more efficient usage, or more new and as yet undiscovered sources, then all the more reason to get involved in political and economic policy instead of, say, reading about celebrities or playing chess (not that I don't like chess myself).
To me, the better technology there is, the more "resources per person" there is. Thousands of years ago, they didn't have solar, nuclear, wind power, or even agriculture, so "resources per person" was low. Thousands of years from now, they will have who knows what kind of technology (maybe even man-made stars), so "resources per person" will be very high. The key difference is the amount of technical advancement.