I was always taught when studying American or World History that the Monroe Doctrine was issued by the US to stop the spread of European imperialism in the New World. But, my question is, why did this work? I mean, at the time it was created, the US wasn't nearly as powerful as any of the European powers, with their massive empires and all, so there was no reason for Europeans to fear America. The European powers seemed perfectly content with getting into wars with other, weaker nations to expand their empires. So, given all that, how did the Monroe Doctrine keep the New World safe from imperialism? It's just something I've always been curious about.
The simple answer is that it didn't. European powers intervened in Latin America throughout the 19th century. France intervened twice in Mexico, including installing the hapless Archduke Maximilian as Emperor of Mexico. Britain took the Falklands/Malvinas without worrying much about US opinion. Britain and France both intervened in the River Plate during the 1838-48 period. In each case, it seems that the Europeans' motives for intervention and withdrawal were a combination of their own imperial interests, and the situation on the ground in Latin America.
If they didn't intervene more, it is almost certainly a matter of opportunity costs. There were so many other uses for imperial resources that conquering and administering famously unstable territories in the New World did not seem like a good investment. Navies could always be put to profitable use elsewhere in Asia, Africa, the Mediterranean, and so on. The parts of the Americas they already controlled (Canada, most of the Caribbean, the Falklands) served their strategic purposes.
The opinion of the United States does not seem to have been a decisive factor in European intervention until well after the Civil War, when it became clear that the US was a major military power capable of challenging European Navies. Around that point, the Monroe Doctrine shifts into its Roosevelt Corollary mode, and the US itself begins extensive interventions in the Caribbean. In some cases, they were acting as a proxy for joint US/European interests in getting bonds repaid, preferring to intervene themselves rather than allow European gunboat diplomacy in "their" sphere of influence.