It's been predicted that once we reach a certain point in time (e.g. 2050), human population will begin to decrease and eventually stabilize rather than continue to rise indefinitely. The reasoning is that as more and more people have access to education and thus middle class wealth and lifestyles (developing countries become 'developed'), the average birth rate will fall. This is already happening in many western countries, where immigration is the only thing keeping populations stable. If this is this case then a Chinese style population control program would be unnecessary. However, spreading education to many developing countries is easier said than done. The result: Bangladesh, as one example, suffers from extreme overpopulation and one of the highest average population densities in the world. This has already contributed to more disastrous catastrophes numerous times in the country. The '91 cyclone killed ~200,000 people because, among other reasons, there were (and still are) thousands of people packed into every square kilometre along the coast. Overpopulation will likely not reach an unsustainable level, but this doesn't negate the fact that it still causes certain problems now. Food for thought I guess.
What you're describing is stage 5 of the demographic transition model, where reproduction rates decline as the standard of living increases. There's actually some evidence of a stage 6, where reproduction rates start to increase again in some advanced countries (but not Japan).