1) Democracy for China. It has been suggested my many economists that economic freedom is a requisite for political freedom. China might just get a serious push in the political freedom category as their economic freedom also get unleashed.
2) The end of world hunger... or at least, more massive reductions of it. People don't like to admit it, but world hunger has declined radically in recent history. You'd be pretty hard-pressed to find a serious researcher, or any bit of serious research that disagrees. If current trends continue, we'll see more drastic reductions in world poverty, and if they accelerate, we could see the literal end of world hunger and/or absolute poverty.
3) Technological progress. This one is an easy one. The already developed world will continue to see more breakthroughs in technology. And as countries like China make their way into the developed world, they'll start pushing through new breakthroughs that we can all enjoy. Think about it this way, if China gets more industrialized, that's less people that have to worry about food and housing, and more people working on a cure for cancer and future computer technologies. Other country's progress is the world's progress.
4) American imperialism will start coming at a higher and higher cost of living standards, and war will become less and less popular. The sentiment of the many will usurp the few special interests who gain from war, and the United States will be forced to reign in its militarism.
What I'm pessimistic about in my lifetime:
1) As more and more country's develop, they're also becoming more capable of building the kinds of weapons that create massive amounts of destruction. Although I think Iran is certainly not very likely to attack Israel or the United States with a nuclear weapon because there's simply nothing suicidal about their current administration, these overreactions to Iran are indicative of future, much more likely problems. North Korea attacking Japan is much more likely than Iran attacking Israel, because they have a much more volatile attitude, and Japan is not equipped to respond in a nuclear way. This is the kind of situation that will inevitably become more common, and how much damage will be done before a peaceful equilibrium emerges, I estimate is much more than zero.
2) I'm pessimistic about the potential for democracy to work well. More countries are going to become democratic, and while that's usually a less bad situation for them, democracy does not solve all problems. Voters simply do not have any incentive to give serious, honest thought to the outcomes of policies. They will concern themselves with and vote for theatrical characters who they identify with leadership, intellectualism, and other other personal traits rather than focusing their effort on knowing more about what they're talking about. While some combination of oligarchy/democracy will provide better results, democracy will continue to be worshiped in a a thoughtless manner.