The future belongs to those who believe they have a place in it. I believe that I do, my country does, and that all people do, regardless of race, creed or origin if they believe in it.
The following is a hypothesis. No value judgments are meant by the following. I say this because it is a rather large set of predictions about the future of our world.
More specifically... hmm. I think the future will be greener, cleaner, and that there will be a sorting out of peoples with higher fertility rates as opposed to lower ones; we can look forward to higher rates of religiosity, an increase in the number of Indians, Muslims, Catholics, Evangelicals, Africans and Latinos relative to atheists, East Asians and Protestants (no offense meant to ANY of these groups), and, despite misleading statistics of a decrease of religion in the USA (totally explained by the fact that most Americans switch religions and during the inter-faith period of their lives, they are marked as having "no religion", but usually end up switching to a more intense version of the faith), I can predict a rise in religious values in many countries.
But before this happens, there will be a "lag" of irreligion/atheism, fueled in part by Europe's influence, party by judges and lawmakers who grew up during the counterculture days, and the fact that, as an exception to the rest of the world, Europe, Canada, Australia and New Zealand are, for the most part, less religious than the majority of the world, for better and for worse.
Old neocolonial ties and powerful institutions in Europe (The Hague, all those institutions in Geneva, the emerging offices of the EU, etc) will still continue their "institutional stickiness", but eventually, the pressure of a decreasing population in Europe, the increasing population in the USA, a continued shift of economic power to American and "emerging" markets, as well as the rise of evangelical and pentecostal Christianity at the expense of "mainline" protestantism will all be too much for Europe's influence to handle. It will still remain a rich continent, but will find itself increasingly sidelined in the next 50 years. The only chance for it to check or reverse this is for the EU to be super-effective AND for the population declines to reverse themselves.
China will overtake the rest of East Asia in economic size; it is about to overtake Japan. It probably will NOT overtake the USA in economic size or military power, although it will try. Japan will see a massive fall in population, economic power, and productivity as it increasingly becomes a land where excellent TVs and cars and designed, only to be made elsewhere. India has great potential, but most of it is still a vast sinkhole of poverty, sadly. I'm not sure what will come of it other than it will claim the title of the world's most populous nation in the next 10-15 years, probably.
The Islamic world will continue to run on oil. When it runs out, or is no longer enough to support them, there will be a great crisis. Dubai's implosion is less than the tip of the iceberg as to what awaits them. Unless they implement effective democracies, eliminate terrorism and corruption to the best of their ability, and diversify their economies beyond oil, gas and "bubble" investments, they are in for a long nightmare.
Africa has so many issues, I need a separate thread for it. Poverty, corruption, crime, terrorism, rent-seeking behaviors, plagues, tribalism, illiteracy, extreme disparities between rich and poor, drought, poaching, and over-dependence on aid are just some of the many problems.
As for the USA, I see us as the major world power 50 years from now, with our leads increasing against all other nations except for China. Our overall lead will be greater, our productivity higher, and our population larger. I see states like Texas, Georgia, Arizona, Tennessee, North Carolina, Utah, and (after they solve real estate issues) Nevada and Florida as being the fastest-growing states. While some of them might go democratic on occasion, most of them will continue to vote "red." It is also quite possible that Texas will overtake California as the most populous state in 50 years.
My own state of New York will likely stagnate unless the city undergoes a boom. I don't know where NYC will be in 50 years, but if the rival cities of Tokyo, London, and Paris all decline (a distinct possibility with the falling populations in those areas), New York stands to gain from their relative falls.