How much of this planet do we each need?

As the disruption to air travel - resulting from the foiling of the "alleged" terrorist plots on 10/8 - starts to abate, I began to wonder whether there was any other way to better organise ourselves on this lovely planet.

The earth is 8,000 miles wide, the world population is 6.5 billion humans, and earth's area is 510 million square kilometers (200 million square miles). Therefore the world-wide human population density is 6500 million / 510 million = 13 per km² (33 per mi²), or 43 per km² (112 per mi²) considering that humans live on land, which forms 150 million km² of the earth. This density rises with the population growth, and some people think there is a limit of what the Earth can support.

So each of us could have our own piece of land measuring 500 feet by 500 feet, and as long as we didn't do anything on our land that impact any of our neighbours, we would all get along famously...

It seems like a big enough space, but if only life were that simple!! So what spoilt it? What didn't might be an easier question to answer...