Answer by Balaji Viswanathan, history buff:
Here is my three-by-three take on the U.S.:
Size: It is the fourth-largest in area and third-largest in population. Countries with greater area than the U.S., such as Russia, have way too much unusable land. The two countries bigger than the U.S. in population, India and China, are still climbing up from the colossal destruction faced in the 19th and 20th centuries and also face severe resource constraints. Russia has still not settled in terms of governance. Brazil and Canada have too few people. That leaves the U.S. in a nice sweet spot.
Isolation: Guarded by two oceans and a frigid nation to the north, the U.S. never had to worry about a major war on its borders. Apart from the Pearl Harbor attack, most of the U.S. military operations in the past century were far outside its territories. Most other nations sit close to their fiercest competitors (China-Russia, India-China, India-Pakistan, China-Japan) leading to insecurity and poor decisions.
Self-sufficient: The U.S. is probably the one country that is fairly self-sufficient in all fundamental resources. Unlike China, Japan, Germany, or India, it has large quantities of oil and gas. Unlike the Middle East, it has plenty of water and agricultural land. Thus, throughout the 19th century, the U.S. grew unimpeded, depending on Europe only for the luxury things.
Flight of the smart: Throughout the ages, the U.S.'s remote location helped cherry-pick the immigrants. Other than Mexican immigrants, everyone else had to travel across oceans to reach the U.S. That made the inhabitants self-selected—the less ambitious ones were left behind. The Puritans, Italians, Irish, East European Jews, and Asians all added faster and faster growth as hard work was a matter of survival for each group (returning back was not an option). The U.S. developed key ideas on the back of its immigrants.
Education: For each wave of immigrants, education was a top priority. Whether it was the Puritan clergymen who created Harvard or the Ashkenazi Jews who immigrated in 1930s and 1940s or the Asians who immigrated more recently, getting to the top of the ladder through education seemed both possible and mandatory. Thus, the U.S. built itself up as the world's education superpower, with a huge concentration of top universities.
Naturally entrepreneurial: If you had to move this far and then stead a random piece of land in the middle, you need to be naturally entrepreneurial. Every country has its noble class. Since Americans don't have Europe's aristocracy or the Indian caste system, they created their own hierarchy based on entrepreneurship. Getting rich became the mantra, and people were ranked by their riches. It celebrated its entrepreneurs like no others.
Right leaders at the right time: U.S. leaders were quite good by world standards. Despite all their complaining, they never had a leader like Stalin, Saddam, or Mao. More importantly, the U.S. was fortuitous in its timing: FDR during the Great Depression, Lincoln during the Civil War, Theodore Roosevelt during the early 20thcentury expansion.
Stability: The present governments of China and India are less than 70 years old. The U.S. is about 240 years old, and that kind of stability is lacking in much of the world.
The wars: By the start of the World War I, the U.S. had built up a massive economy. During the war, it finally announced the "secret" to the whole world. Although the U.S. faced some destruction, in relative terms it got far ahead of the rest of the world (most of which was obliterated). It was a victor in both the world wars and spared of the ignominy faced by Germany and Japan.