Either there will be disintegration leading to more countries or federations leading to less countries. Depends on how optimistic you are. I'm not very optimistic at all, so I vote for disintegration and chaos, primarily in Africa (look at an ethnic map of it sometime!) but in other places as well.
I would go a step further and say both. Some areas will see break up and others stronger federations. In some places it may look like both happen.
In areas that have artificial, generally dictatorial, nations, there will be a strong tendency for autonomy and breakdown of the old nation. The Soviet Union and Yugoslavia were 20th century examples. I agree that Africa may have some likely examples in the coming years, Eritrea may have been an early example.
A different kind of breakdown may result from areas that see greater local autonomy from traditional strong central government. By mid-century the population boom in Asia will have reversed, and I can see city-states act as semi-autonomous regions within their traditional countries. Economic factors will drive the central governments to allow this over a lengthy period of time.
Some existing economic federations may well become tighter, but the need for places like the EU to become as close knit as the US doesn't exist in the 21st century as it did in the 20th. Global factors will permit a successful multi-level government. Macroeconomic coordination can happen at the super-national level like the EU, but there will be a strong need for more state-level coordination beyond the traditional federation. With this model, a European state may set up special trading arrangements with an African state, independent of all but the most important federation decisions.
Another important federation will not have any traditional boundaries in the coming century. In just the first decade and a half of the Web, communities have arisen that follow none of the traditional boundaries. The next step after individual associations are associations of local governments. I can imagine that the loose relationships of sister cities today, become a model for for new semi-global federations in 50 to 100 years. Global alliances will be based on economies, culture, religion, recreation, and I'd expect many other factors.
It may well be that in 2100 it is hard to speak of nations as we do today. There will be more unique levels of governance both larger and smaller. The nation-state of 1600-2000 would not then have the same all-encompassing role.
