Maximum world population

It depends on how each person uses the resources that they have access to

And also where each person is willing to draw the line on their personal needs

My guess is around the 6 Billion mark plus (at our current technological state)

Note that certain groups are in the process of de-populating the Earth and have been for quite some time. Consider which countries have been involved and benefitted from War in the past and today. Various pandemics, AIDS, SARS, Avian Flu, etc. have been known by some to have been intentionally released. They are also far too specialized (targetted) to be completely natural.