I can't really answer your larger question, but one specific example of what you're asking about occurred in Iran in 1953. The CIA overthrew a democratically elected prime minister, Mohammad Mossadegh, who was poised to usher in a new era of government by the people in Iran. Unfortunately, the CIA overthrew him in a coup for a variety of speculated reasons. Mossadegh nationalized the oil industry in Iran which Britain had previously monopolized, one of the large political parties in Iran was communist and there were speculated or perhaps fabricated ties between it and Mossadegh, and finally the U.S. had a very good working relationship with the existing Shah of Iran, Mohammad Reza. Ultimately, the coup is largely credited to have been caused by fear of communism spreading to Iran and Russia gaining another foothold. Whether that was likely to occur is debatable, although that in itself is getting into counterfactual history. An important consequence of this event is that it set the stage for the Islamic Revolution of 1979 in Iran. The result of this event is the current government in Iran and the very unstable political relationship between it and the U.S.
A good source on this specific subject: All the Shah's Men - Stephen Kinzer
These answers by /u/ainrialai may interest you. Together, they provide a general overview of American involvement in his area of expertise, Latin America.
American foreign policy has traditionally focused around two objectives depending on the era: isolationism and stability.
Early American foreign policy followed Jefferson's oft quoted warning that the United States should avoid entangling alliances. This was popular. The entire premise behind isolationism is that the United States should avoid becoming a colonial power in favor of manifest destiny. However, this was always a theory rather than a practice. As early as the Monroe Administration, the United States took a stance in favor of stability in the form of the Monroe Doctrine which declared that the United States had the right to intervene in any colonial conflict in North or South America in favor of states seeking independence from Europe. The Monroe Doctrine was largely scoffed at by Europeans with one key exception: HM Government tacitly agreed to uphold the doctrine. This may sound bizarre given that the United States was by then hardly 30 years old, but you must also remember that several leading Englishmen also lent support to the Revolution and there were multiple debates on the freedom both in the Lords and the Commons during this era.
Since the United States feared sharing a border with the overseas territories of the Great Powers, it began to intervene in Latin America as the United States became increasingly more powerful and stable throughout the 19th century ultimately culminating in the Roosevelt Corollary in 1904. This document stated that the United States had the right to intervene in Latin America in cases where Latin American nations were acting in contrast to American interests. This isn't to say that Roosevelt was promoting colonialism, but rather the ability to enforce the earlier Monroe Doctrine: should Latin American be threatened, America should have the right to intervene. (see: Venezuelan Crisis) However, this did have the effect of reducing Latin America to a sphere of influence of the United States which of course led to increasing levels of foreign intervention.
As early as the 1850s, Washington had ordered several minor interventions in Latin America which led to a taste for increasing levels of serious interventions. The first, which may surprise many, was in Buenos Aires when the Marines landed in order to prevent an insurrection at the request of the Argentine Government. In 1854, the United States Navy shelled Managua in retribution for offending the US Ambassador to Nicaragua. These two events sound far more aggressive than they actually were -- 19th century international affairs revolved around gunboat diplomacy.
The first major American intervention overseas (aside from the Barbary Coast, where there was no intent to change the administration rather than protect US shipping interests) was the Boxer Rebellion in China. In 1910, the US straight up occupied Nicaragua leading to a series of American occupations across Latin America: Haiti, etc. were all occupied. This finally culminated in the American Expedition to Europe in 1917.
It's important to note that all of these early interventions were, by 19th century standards, rather tame. They did in fact protect American interests and, often enough, also did help enforce stable rule in South America. (This conclusion does not include actions relating to Manifest Destiny). Having said that, American intervention became increasingly imperialist after the First World War as the United States became the world's premier economic power. The virtual bankruptcy of the British Empire during World War One led to Americans taking up the slack and, by 1945, American foreign policy had evolved into acting as a referee. By the time Acheson wrote NSC-68 during the Truman Administration, it had become apparent that referee would not be enough to contain the threat posed by the Soviet Union thereby adopting a hawkish foreign policy towards communism.
From NSC-68 onwards, we can see US foreign policy reformat itself into a more aggressive stance. /r/drrickmarshal already expounded on Mossadegh, and NSC-68's impact meant that any vague move towards socialism or the Soviet Union became an immediate concern for the Americans -- a move that sometimes backfired. In short, there is no grand conspiratorial schema in terms of how the US has intervened but rather a series of policies that have built upon one another from the Federal Era to today.
You might enjoy Legacy of Ashes: The History of the CIA by Tim Weiner. He's not a historian but is a reporter on intelligence activities and based the book on tens of thousands of documents from the CIA archives and interviews with hundreds of CIA veterans of all levels.
The book covers the CIA from its founding to the War on Terror (it was published in 2007), and details CIA involvement in the overthrow of the governments of Syria, Iran, Guatemala, Indonesia, the Congo, Iraq, the Dominican Republic, Vietnam, Brazil, Ghana, Chile, Argentina, Turkey, and Nicaragua as well as covert action in Greece, Japan, Eastern European nations, Afghanistan, Poland, Cambodia, Angola, and Cuba. I'm probably missing some, this is going by memory.
The extent and nature of the CIA's involvement in these places varies widely from funding cultural organizations that acted as fronts to supplying and arming actual troops, but the number of nations the US has toppled or affected via covert action is huge.
The U.S. has a long history of staging coups d'état, either through direct military action or through covert activities by the CIA. Dozens of countries have been targeted, some repeatedly.
In the early days of the republic, the U.S. was mostly preoccupied with westward expansion and possessed only a fledgling navy. But from the 1890s on, the U.S. turned outward and began to overthrow foreign governments at the behest of American businesses, or when it would benefit U.S. naval and trade power.
1893 - Overthrow of the Kingdom of Hawaii (a constitutional monarchy), led by a small group of foreign businessmen, and helped by U.S. troops called in by the American diplomat to Hawaii (acting outside his authority). Nevertheless, with the next presidential administration Hawaii was annexed.
1898-1934 - The Banana Wars - Many interventions during these years following the Spanish-American War. Some nations were occupied continuously for decades or saw U.S. intervention half a dozen times, often driven by the interests of American fruit companies. Gave rise to the term "banana republic".
After assisting Cuban and Philippine independence movements against Spain, the Americans became the new colonialists, occupying Cuba multiple times and brutally subjugating the Philippine Republic (1899–1902).
1903 - Teddy Roosevelt used "gunboat diplomacy" to get his way when the Senate of Columbia refused to give the U.S. a perpetual lease on the (then under-construction) Panama Canal. Naval support and marines helped Panamanian rebels break off from Columbia.
1912-1933 - U.S. occupies Nicaragua in order to prevent the construction of any other canals.
1934 - FDR implements the Good Neighbor policy, pledging non-interference in Central American affairs.
1944 - Old habits return, however, at the conclusion of WWII, when countering Soviet influence is deemed more important. By this time, it's become less socially acceptable to roll up with gunboats and send in the marines. From the Cold War on, covert operations by the CIA become more popular means to depose leaders.
The number of CIA interventions is much longer than the ones already listed, and the more egregious examples of overthrowing stable democracies were explained in more detail already, so I'll just leave the Wikipedia link: Covert United States foreign regime change actions
A variety of methods are employed, including propaganda, supplying weapons, training and money to rebel groups, or orchestrating assassinations and coups d'état.
A great source on this Killing Hope by William Blum. It is on CIA military interventions post wwii
