Cuba is under a US-sanction from 1958.
Why hasn't this sanction been able to do much damage to Cuba's communist regime?
What about Venezuela?
Generally speaking external sanctions do not substantially affect a ruling elite directly. They can have a secondary effect e.g. oil sanctions reducing bribe opportunities, but these weren't a large factor with Cuba.
For sanctions to cause the effective removal of a ruling group, a number of factors need to come together:
In Cuba, there had been a number of unsuccessful attempts at uprisings, the Bay of Pigs probably being the most famous. But it's not evident that the majority of the population considered the Castro regime at fault for the US sanctions (the blame was, not surprisingly, attributed to the US). There was widespread dissatisfaction with the Castro regime but the same can be said with, say, the Bush or Thatcher regimes: enough for tension but not outright civil war.
It's also worth remembering that, until the fall of the Soviet Union, Castro had significant international support. It wasn't until the fall that Cuba became substantially isolated and that did, in fact, lead to a slow thawing of relations with the West.
US has already caused a lot of harm towards Cuban by imposing the indirect sanction rules that forbid any ship that docks in Cuba seaport from docking in any US port for at least 6 months. That destroyed a lot of Cuba trade, and this even strengthens Castro propaganda that USA going to enslave Cuban, again. (Though Obama administration has lifted the embargo lately)
There is little incentive for Cuba public to revolt: there is more than enough terrible examples of central and south America counterpart. For example, Central America Banana Republic like Honduras, Guatemala prove the "free world" is rather disastrous. Neo-liberalism economy in Chile shows that the Chilean "free economy" but dictatorship regime murder a lot of dissidents.
Ironically, contradict to US propaganda machinery, Cuban dissident rarely smackdown(or even murdered) compared to Central and South American counterparts.
And there is one more irony: the prisoner in USA detention camp in Cuba Guantánamo Bay provide free health care to counter Castro socialism free health care. So perhaps someday, the cheapest way for United state citizen to get free health care is going to jail.
Additionally to Alex's answer, the embargo is far less likely to work if it's ineffective in preventing other major powers from engaging with the country. Most notably,
Cuba has been USSR's (and to a lesser extent, Russia's) client state.
This included enormous amount of economic aid and trade. (source1, source2). For a really excellent overview, see "The Political Economy of Cuban Dependence on the Soviet Union", Author(s): Kosmas Tsokhas, Source: Theory and Society, Vol. 9, No. 2, Special Issue on Actual Socialisms (Mar., 1980), pp. 319-362 Published by: Springer; Stable URL: http://www.jstor.org/stable/656859 .Accessed: 07/06/2013 15:56"
Venezuela hasn't ever been "embargoed" in the first place, by US or anyone else, and they enjoy strong relationships with Russia, and most of anti-US block both in Latin America and elsewhere in the world.
Understand that when we talk about embargoes, we need to understand that it typically doesn't mean a full-bore embargo (i.e. a military blockade preventing any trade whatsoever). So Cuba was excluded from US markets but they could still get some supplies from other countries. And if we really wanted to turn the thumbscrews to Venezuela we could embargo their oil. We don't do that because the effects would be devastating to the people of Venezuela
The Trump administration introduced sanctions Friday to prohibit Venezuela's national leaders from accessing U.S. credit or selling bonds to Americans, but specifically and purposefully don't hit the country's oil industry.
So the embargo against Venezuela is more for show and to tighten screws to express our displeasure. Which is basically what the Cuba embargo does/did. They hurt, but it's the political equivalent of a bloody nose. Real regime change requires boots on the ground, which the US is reluctant to do for obvious reasons
Country restructures its economic for resist embargo: become more self sufficient, create stuff local, consume resource more efficient, use less resource, find new trade partners, indirect trade around embargo, etc.
Also often hard force people follow embargo. Hard know where ship will go/come if not follow it (too many ships). Embargo countries not stamp passports or no have paperwork for help defeat embargo, fake documents, mark products from different country (when have government support many things become possible). Many people hate embargo and think it immoral/hypocrisy (outside and inside embargo country) and help find/create ways around it.
In the case of Cuba, the embargo has partially worked. To know about the damage of the US embargo (or blockade) and other actions you can read the Demand of the Cuban people to the government of the USA for human damages.
You also can read the resolution that Cuba presents every year in the UN and wins by a majority in favor of the remotion of the embargo. That resolution contains data about the damage in the last period.
The USA has historically regarded Latin America as part of its sphere of influence, it's back-yard; this harks back to the Munroe doctrine formulated in the 18th C that recognised its position as regional hegemon.
Latin America, like many countries outside of the West was historically associated with Socialism; in this, it is similar to the countries in the European mainland which after much agonising chose the Social Democracy as a political paradigm to underpin their societies. It's also notable, that unlike the United Kingdom and the USA there were strong communist movements in both regions - and so a respectable position; whereas in the UK, it was seen as eccentric, and in the USA, reprehensible and maybe even treacherous. At no time, were British people told they were Anti-British for holding on to such views, nor did they set up a political inquisition to investigate charges of being Anti-British. This is quite unlike the experience of the USA where sympathising with communist or socialist aims were seen as Anti-American - a revealing turn of phrase.
The embargoes on Cuba & Venezuela was part and parcel of the USA policy of containment; that is to contain the communist menace, and also it's less militant cousain, socialism; in many ways the USA policy succeeded: the collapse of the former Soviet Union, the turn of Communist China towards Capitalism; the meddling in the domestic affairs of Latin American nations, Chile, Cuba, Nicaragua and Venezuela most famously amongst them succeeded in pushing back the Socialist menace there too.
The Cuban revolution had been a great inspiration to Latin America; it showed that political situations were not carved in granite and could be changed; Eduardo Galeano observed that given the success of the Cuban revolution the USA would not allow another socialist experiment to succeed in Latin America; And so it proved, neo-liberalism was imposed as an economic orthodoxy on Latin Anerica. Socialism as well as Communism was to be contained, and then crushed.
The turn of Latin America towards Socialism again was in large part due to the failure of these economic doctrines, the growth on inequality, and the highly polarised societies that resulted; they succeeded in taking the political initiative as the centre and focus of USA foreign policy - after the collapse of the Soviet Union - was taken up with the Middle East.
It's worth noting that the economic embargo on Cuba goes back some time; the Platt amendment to the Cuban-American treaty of 1903 restricted Cuban economic and political freedom, and this lasted until Castros revolution; the embargo that the USA placed on Cuba merely reinforced their historical antipathy to Cuban independence and was in line with their politics of containment; this forced Cuba into the Soviet camp during the Cold War and probably ensured their survival; certainly, they went through a difficult time after it's collapse and many predicted the final collapse of Cubas revolution. This has not happened, and is unlikely to happen now, it's too central to Cuban identity. The Council of Foreign Affairs noted in a recent report that the days of USA authority as regional hegemon were over with the nations of Latin America reaching out to newly burgeoning economies like India and China.