I think that World War II affected the United States more than Latin America.  It was predominantly a European war, and while the Latin American countries had ties to Europe as colonies, they were not necessarily strong allies.  The United States was an economic power, and therefore influential.  It made a large contribution as an ally to Britain before even entering the war formally.

Very good point in post #3. I would add that I doubt that any single Latin American country has the good fortune to have such a vast supply of physical riches to draw on. Before WWI we were already developing into a powerful country. Remember, at that time we had less in the way regulation and everything was a wide open race to achieve success. It didn't work out well for everybody, but it did lead to a lot development.

I agree with the previous post, but it should be noted that the United States had a hand in creating the conditions necessary for rule by strongmen. Indeed, in many cases (Trujillo in the Dominican Republic, Somoza in Nicaragua, possibly Pinochet in Chile, Batista in Cuba, a series of dictators in Guatemala, and others) the United States supported and propped up these strongmen, sometimes with military force. Often, US intervention coincided with business interests, as in the infamous case of the United Fruit Company in Guatemala. It would be far too simplistic to say that US policy created the conditions described in the original question, but certainly it is worth noting that the corruption, violence, and dictatorial governments that plagued many Latin American nations in the twentieth century sometimes occurred with American support. 

It is because of how they started out.  After all, the US was more prosperous than the Latin American countries long before WWII.  Basically, the US was more prosperous because it was democratic and capitalistic.  The Latin American countries had strongman rule and economies that were heavily regulated by the government to help the cronies of those strongmen.  The US had a much more open economy and political system.  This it the main reason for its prosperity.