Never did America experience a coup, a dictatorship (in the sense of a strongman rulling against the wishes of the voting citizens) and only once did it experience a civil war. Countries like Argentina, Venezuela, Colombia, Mexico, Peru and to a lesser extant Brazil (only because it was a monarchy in the 19th century) all went through those hazards much more even before the Cold War. Why is that so? I know the US became a developed country earlier, but even before it started inustrializing it was already a stable reoublic. So why?
So, a lot of people have tried to answer this question. There are many interpretations as to why Latin America and Anglo-America have turned out so very differently. One rather comprehensive explanation that I can recommend is that which is put forth by Bradford Burns in his collection of essays The Poverty of Progress. Overall, the argument is that Latin American political and economic elites were more apt to subscribe religiously to European ideals of social and economic progress. For much of the nineteenth century, Britain was the center of the economic world because of its early start on industrialization in the north of England. Their adoption of Smithian economic liberalism, which included the prohibition of government intervention in the economy as well as the belief in the comparative advantages of nations, led to their promotion of a specific economic model. This model had Latin American nations as being rich in natural resources like copper and iron for Chile, wheat, beef, and wine in Argentina, silver, cochineal, and corn in Mexico, or wool in the Andean highlands. Britain's comparative advantage, meanwhile, was their industrial capabilities. This made most Latin American countries into export economies, which greatly benefitted the ruling political and economic elite in these countries but led to the bulk of the population to poverty. The religious belief in comparative advantage led the elite to scuttle any attempts at industrialization. The United States, however, resisted attempts to fully commit to the Anglo-centric world economy at the time and allowed heavier industry to develop, especially in the north. Meanwhile, it was not until the global economic crisis of 1929 and 1930 that classic economic liberalism was so discredited that many Latin American nations began to develop industry of any note.
Regarding political stability, Burns has a somewhat questionable explanation for that. He claims that Catholic societies inherently seek for paternalistic, strong leadership, and actually seek out strongmen with a connection to "the folk". While I don't entirely subscribe to this, the case is different in each country. I study twentieth-century Argentina, and in that case it has to do with the battle between the forces of traditionalism and modernism, between the forces of authenticity and cosmopolitanism. The military tended to see themselves as representative of the former. Because of the lack of Catholic nationalist influence on the US as well as the fractured state of Protestantism, the ideas that justified dictatorship never took hold in the US like they did in Argentina, among other countries. Yet again, the reasons are different on a case by case basis, and there are many explanations to see why certain political and economic process take hold in one country but not another.