The future is incredibly difficult to predict. Honestly, if we go back 200 years ago, who in their right mind would have predicted that the USA would one day be the most powerful nation in the world?? They'd have told you that you're crazy to suggest such a thing.
That being said, who is the most dominant nation on Earth 200 years from now? I have to base it on current trends (historically, that's a lousy way to predict ANYTHING). Because nobody can pose an immediate threat to the USA, that means that they will remain relatively dominant for a long time. Under current trends of immigration into the United States, most anything can happen. Personally, I think that the United States remains a major player, but that their dominance will gradually diminish. Their fortuitous location becomes the secret of their success.
China can surpass the USA in economic and military strength. Perhaps surpass the USA and Europe in technology. But they are surrounded by counter-balance. For every bit of progress made my China, India will do its utmost to match it purely for their own self preservation. I think that India and China will become the two most powerful nations in the world and that their proximity to one another will be their greatest limitation. Also, as China increases in strength, Japan, the Philipines, Vietnam, Thailand ... everybody else in the region forges alliances and plans for every contingency of China turning conquerer. The more powerful China becomes as a singular entity, the more driven those who have reason to fear them are to keep up.
The European Union looks good on paper, but seems to be plagued with problems. They could be the biggest, baddest thing in the World pretty easily if they can figure out how to unite themselves in an effective manner, especially if the EU can expand.