A little history lesson as far as Chile is concerned, first:
In 1973, the chilean military performed a coup d'etat and removed the democratically elected government of Salvador Allende from power. The military government in Chile lasted between 1973 and 1989, year when the military junta returned power to the political class after losing a national referendum about its continuity. During the military government, an estimated 3,000 political opponents were murdered by the authorities, and tens of thousands of others were tortured.
Now, for what other people won't tell you: The government that was taken down in 1973, was a communist government that was basically crushing the soul of our country. Thanks to president Allende's atrocious economic policies, people had to queue up for hours to be able to purchase bread, social unrest and violence were commonplace, and we were quickly turning into another Cuba. The country was completely broke, our agricultural production crashed, and we only had enough foreign currency to keep on importing food for a few more weeks by when the military coup happened. Many prominent politicians, people who were and still are left-winged, backed the military coup back then. Despite its bad Human Rights record, the military government let the economy be run mostly by professional economists (the 'Chicago Boys', a group of economics graduates from the University of Chicago), which set the floor for a solid basis of growth for decades to come, and is largely responsible for the excellent Chilean economic performance in the 90s. A new, better constitution was drafted, and all in all, the military government turned a wreck of a country into a country that later flourished as a shining beacon in Latin America.
In 1989, the Concertacion came to power, a political conglomerate of the center-left. They handled the democratic transition well, provided growing social stability, reaped the fruits of good economic policy in the form of sustained growth, and all in all were a good thing for the country. As the years dragged on, economic growth slowed from an average of 7% per year, to about a 3% a year. Crime flourished under the Concertacion's watch, roughly doubling in frequency every 10 years (after correcting for population growth). Our education system was terrible, and despite more and more spending, it wasn't getting any better. Unemployment was high, and it wasn't going down. Getting health care could take upwards of 6 months. The size of the government and taxes kept going up, but they kept getting many of the basics wrong. Note that it was still much better than what other countries around us were getting, but the country was on the wrong track. There was too much corruption in the public sector, and it was time for a change.
And now, after 20 years with the Concertacion in power, change we got. Sebastián Piñera is a businessman, who voted and campaigned for the end of the military government in 1989. He leads the right-wing party Renovación Nacional. When he won the elections, his left-wing opponent and ex-president (1993-1999) Eduardo Frei congratulated him, shook his hand, and wished him luck. There were no riots in the streets, and no return to a military government like the other thread here suggests. The elections were remarkably peaceful, the results transparent, and the country seems ready for some change. In particular, I'm hoping Piñera will do a better job of handling corruption, education, health care, unemployment and crime, which the Concertacion had objectively shitty results in.
This is Chile, and this is our new government.