The common perception among many Americans is that China is our next real competitor. Many fear that we will be passed by economically or militarily about the middle of this decade, due to China's enormous population. Those who fear China are correct in pointing to demographics as a major determinant of relative national power, but they might be surprised on what the demographics actually tell us on a relative basis. Here's a plot of the populations of the major countries that will be driving population growth over the next 50 years.
There are a couple of items that are striking. The population of China is already growing at a slower rate than that of the United States. Further, over the next 50 years, the total population of the US is expected to grow more in absolute terms than that of China. Indeed, the population of China will begin to decrease around 2030 and will be surpassed by India around 2035.
While China's economy currently is growing at a very rapid pace, short periods of stagnation or even depression are probable. In China, these short periods have led to political instability. For instance, only a couple of years of subpar growth led to the democracy movement and Tiananmen Square crackdown. So one possibility is that the dictatorship will collapse and a more acceptable system of government will take hold. The Chinese will have to one day face the fact that dictatorships aren't that durable of a way to run a country.
Another very real possibility is that China's growth will moderate somewhat--let's say to a rate slightly above that of the US. If this happens, then the US doesn't need to be too worried, since China's economy is only about 60% the size of the US economy (adjusted to Purchase Power Parity) and is still decidedly low tech for about 3/4ths of the population.
Lastly, India could overtake China as our main competitor. India's population and economy are expected to grow at a steady clip, with the population in 2100 about 70% higher than China's. Educated Indians speak English. India has some very good schools, top notch professionals, and an economy that is fairly transparent. I would consider this a very welcome "competition", considering that India is a democracy and shares many of our values.
In summary, any of the above scenarios could come to pass. History demonstrates that there are often bumps in the road to prosperity, so China's surpassing the US cannot be taken as a given; perhaps not even a probable outcome.
Sources and Notes: Please see my underlying spreadsheet for the raw data and chart. I used the raw data from the Census Bureau's International Database in creating the chart. The UN Population Division also has useful projections, broken out into 3 variants. Please note that in the middle variant, the US population is expected to grow at a continually slower rate. I have my doubts that immigration will be curtailed, which these variants assume. If immigration is not curtailed, then the US could have substantially higher population growth.