The United States occupies the choicest piece of territory on the surface of the Earth. If you could select 3 million square miles of land anywhere on the planet to build your country on an undeveloped Earth devoid of people, you would have to be crazy not to pick the territory that makes up the contiguous United States.
The US is one of the most diverse, fertile and bountiful countries there is. There are vast forests filled with softwood and hardwood trees, the farmland is rich - by many accounts some places in the US produce more per acre than anywhere else, there's plenty of fresh water in the form of rivers (many of them navigable), and plenty of lakes, the mineral wealth is immense... the US has the capacity to grow enough food to support a large population, it's home to some of the finest natural harbours in the world in the form of places such as the New York Bay and San Francisco Bay, and the United States spans a continent, which means that the territory is protected by a pair of vast oceans.
No contiguous area of similar proportions offers anywhere near as much - not Continental Europe, East or Southeast Asia, Australia, or the heart of Africa or South America. Those places are not as temperate, not as fertile, not as blessed with forests or mineral wealth, they don't provide access to anywhere near as much water and they're nowhere near as well protected by natural defences, nor can as many good ports be found there.
The United States was destined to be the greatest country in the world simply based on its geography. The Russian Federation is roughly twice the size of the United States, but Russia has few harbours that are as easily accessible and ice-free in the winter, most of the rivers are not navigable and of those that are, many are useless because they meander into the interior only to flow south of Russia's borders or into the ice-clogged Arctic. The growing season in Russia is far shorter, there are fewer species of trees, and because Russia's river system is inferior to that of the US, there are vast swathes of boggy wetland all over Russia that cannot be developed.
Australia is far too dry to support a large population. Australia relies on imports, and because it cannot support a large population, it has developed much more slowly than other first-world nations so that the level of infrastructure is just a joke. There are few roads and railroads connecting the various centres of habitation in Australia, and it's doubtful that things will change, even a hundred years from now. In centuries to come, the wide majority of Australia will be an empty, desolate, arid desert.
Much of Canada looks like the USA - Canada has wonderful ports and some very good arable land, but the problem is that there isn't much of it. In terms of natural woodland and fresh water, Canada is batting a thousand. But the growing season is short, and Canada was not able to support a very large population during the period when it began to industrialise. Much of its industry is located along the coasts and along the border with the US, and because the US has always enjoyed a larger population, its industry has always been far stronger. Much of northern Canada is empty and underpopulated. Things are changing, but that's only because the established cities are growing larger and growing outward. It's very unlikely that the far north will be any different 100 years from now than it is today.
Lands south of the equator, or those that straddle it are not temperate places. They're lashed by tropical storms, they're home to disease-carrying insects, and they go through periodic droughts.
Besides the fact that the US occupies the choicest real estate, there's also the diversity of its people. The United States has always attracted people who have something to give to the world. Because the United States has so much to offer, and because over time it's become more difficult for outsiders to get in, the United States has been able to select the best people from all over the globe to come and to make the US home. And they've brought their brilliant minds, their industriousness, their blood and sweat and tears. The United States has been responsible for some of the biggest advancements in so many fields over the course of the past 250 years, from agriculture to architecture, from computer technology to medical technology, from airplanes and automobiles to weapons, the US has always been an innovator, and that's primarily because people are free to experiment and encouraged to be bold. The Americans embrace those things more than anybody else anywhere, that's why they stay on top.
The economic, industrial and military might wielded by the Americans puts the USA at the top of the pyramid. Those things give them a level of political clout and cultural influence that dwarfs that of what any other nation could muster.
And although there's a great deal of dissent among Americans when it comes to small things, you'd be hard pressed to find 300 million people anywhere else on Earth that would be more willing to band together and see one another as family. There are some bitter feuds brewing in the US, and there has always been some degree of animosity - the racial strife in the country is practically unparalleled elsewhere, the various political factions are vehemently opposed, but at the end of the day, they all salute the same flag. In Europe, few Britons consider the average Italian one of their own, few Swedes would see someone from Portugal as a wayward cousin, the same is true of people from various parts of the Americas, from Asia or from Africa. There are a lot of Americans. And if they decide to put their squabbling aside and come together to fix something, you had better hope that they aren't aiming to fix YOU.
I don't know what the world will look like in another 250 years, but I can tell you that if the United States is no longer the top dog, whoever earns the spot will have had a Hell of a time doing it.