That's good question--- a huge question, but a good one.

It is hard to generalize, as each country's particular socio-economic factors varied widely, but in a nutshell, the military dictatorships were the elite's response to the pressures from workers and peasants for better pay/more rights/unionization/etc. A good overview of this can be found in the textbook by Chasteen "Born in Blood and Fire"--as the title suggests, the emphasis here is on the violence of Latin American History.

For example, in Argentina, the first military government was in 1930, triggered in large part by the economic depression and the inability of the ruling regime to ameliorate the situation. The later military governments (1943-5; 1955-58; 1961-63; 1966-71; 1976-83) were a response to growing worker mobilization and the unwillingness of the elite and middle class parties to address worker demands without upsetting the economic elite (for more on this see James "Resistance and Integration,' Rock "Authoritarian Argentina," and more broadly something like Romero's "A History of Argentina in the XX century." The Brazilian example is somewhat similar.

The cases of Honduras, Peru, Guatemala and even Ecuador are similar, but have a much more defined racial dimension, as a lot of the social unrest could be traced to a long history of oppression by white and mestizos of the large indigenous population. (for Guatemala, see Grandin's "Last Colonial Massacre," and "Blood of Guatemala," and many others on the 1953 coup-- which was a watershed one).

The second part of your question (why did they end in the 80s?) is even a bigger and more complicated question. Recent scholarship suggests that a growing global discourse on Human Rights forced negative international attention on the dictatorships, forcing them to step down. Additionally, you could mention the successful dismantling of the populist states by the mid 1980s, and the turn to neo-liberal reforms (which undermined a lot of the union-based mobilization power) or the green-revolution (which prompted massive rural to urban migration, disrupting agrarian-based movements). In the Argentina case, the neo-liberal reforms that privatized most state-run companies, and the "retrenching" of the state also had the fortuitous side-effect of disbanding the military (to a large degree), ending mandatory military service and closing a lot of bases, factories, etc.

Hope this helps, and hope someone can provide better answers for the second part and some of the other examples!

One of the primary reasons for the existence of military dictatorships was that the US generally supported and maintained friendly relationships with the dictators.

US involvement is often overstated. But it was almost always there. For example in the 1964 Brazilian coup, the Brazilian generals contacted the US military attaché Colonel Walters and informed them of the planed coup. Walters reported up the chain, resulting in president Johnson authorizing Operation Brother Sam which included using a carrier group based around the the USS Forestall to support the coup. In the end it wasn't needed. And the coup wasn't a US plan at all. But most anti-socialists knew that they had only to pick up the phone and the US would be there to help overthrow a leftist government.

And the US was from the 1940s on, running the School of the Americas. This was a West Point for Latin American militaries, with a focus on counter insurgency. At least a dozen of the Latin American military dictators attended at one point or another.

Again I don't want to overstate the case for US involvement. Most of the military governments ultimately arose from local causes. But when you had a clique of US trained leadership in the local military with a beef with a left leaning government... well they could frequently see plenty of precedent where the US had been happy to support anti-socialist coups in the past. And it made it easy to try one locally. And once in power, the US continued to give military and economic aid to such partners.

As to your side question. As the Soviet state ended, so did the fear of international communism. And with that so did the US interest in anti-socialist dictatorships. Again this is not the only reason, but with one of their supports removed, the dictatorships were weakened.

Sources

Brian Loveman - For la Patria: Politics and the Armed Forces in Latin America

Patrice McShery - Predatory States: Operation Condor and Covert War in Latin America