1900, Argentina was on the verge of breaking out to be one of the most successful and prosperous nations in the world, seen as rivaling the US, Great Britain, Germany and France at that time. However, a socialist government came to power with many ambitions, including programs of social reform on a vast scale. These programs bankrupted Argentina, sending it into an economic tailspin from which it has yet to recover. More recently, the nation of Venezuela, once prosperous and successful due to oil wealth, embarked on a Marxist central planned economy that has failed in a spectacular manner, causing millions to flee the nation and leaving those that remain scrambling to find the basics of life to survive.

But most Latin American nations have failed to find a stable, grounded political path, which is the key toward growth and progress. All too often, disaffected and desperate masses will back a politician (usually leftist, Marxist) who promises to redistribute wealth and reorganize society. Even when these strongmen take over, since many of these nations are tied to some product for capital (e.g., sugar for Cuba, oil for Venezuela, copper for Chile, etc.), world market price fluctuations can wreak havoc in their economies. What we so often see is a political pendulum that swings from left to right. When these ambitious efforts (often by well meaning leaders who lack insight into market economics) fail, the nation(s) experience economic disaster, and this ushers in military juntas that take over the government, suspend many rights, and strive to right a sinking ship. This pendulum swings back and forth, with more military coups, and often a return to democracy. But because the population soon grows disaffected again, the politician who promises the most to the masses, often is elected again, and the cycle repeats itself.

This is a generalization, of course, and each nation must be looked at for the specific story. A nation like Paraguay is very different than Chile, for example, and Chile is one of the more successful stories in Latin America. So is Costa Rica, which is amazing since nearby neighbors—like Honduras and El Salvador—are in essence, failed states (which explains the desire for most of the population to flee their homelands). But Latin America has never, for the most part, found the right combination of economics and government to permit it to move smoothly toward success. There are success stories, of course, but lack of education, poor economic opportunity (tied to banks), and spectacular political corruption (from the top levels down to the local police and officials) have all had a retarding effect, which is a major part of why Latin America lags far behind North America in overall progress and development.

In one aspect, Latin America is fortunate in that it has seen very few wars between the various states. Most are unfamiliar with the "War of the Triple Alliance", or the "Chaco War", or the "War of the Pacific." So unlike Asia and Europe, where millions died from wars, South America has seen relatively few wars. The violence in these nations has been largely internal, with revolutions, coups and the like, so that the threat of violence is more from an internal agent, than one that is external.

This is a huge question because it covers many countries and more than two centuries.  Therefore, any answer can only be a very gross simplification of the actual truth.

There have been two major changes in the political systems of most Latin countries.  First, they have all become independent.  Second, many of them have become democracies at least in name.  The major continuity is that many of them have remained less than truly democratic.  Until recently, Mexico was a one-party state.  Venezuela is ostensibly a democracy but Chavez is a strong man.  These are some examples of the lack of true democracy in the region.

Economically, the major change is that the Latin countries have become richer than they had been.  The major continuity is that many of them are still in what some would call a neo-colonial relationship with the US and other rich nations.  Many Latin countries still have economies based on selling raw materials to more developed countries.