I love this question.
First its important to differentiate our moral obligation from our moral authority.
MORAL OBLIGATION:
Many people argue that America has a moral obligation to help nations/people that need it. This is both because we are a wealthy and powerful nation and also because the sins of our past were the cause of current problems in other countries.
In many cases the obligation involves internation aid, something that America as a country begrugingly participates in. As a government we give a lot of foreign aid, but by percentage we are actually pretty terribad. On the other hand, private donations of foreign aid from the US are exceptionally high in America, equalling or surpassing the amount given by the government annually.
This also involves a desire to intercede in appalling genocides like Rawanda, Sudan, etc., accept immigrants and assylum seekers, or to adopt foreign babies.
In general I would argue that we as a country want to fulfill our moral obligations, but fail quite regularly. Our commitment to global environmental policy is massively fail. We have not gotten involved in some of the most horrific genocides that have hit the planet in the last couple of decades. Overall we do not succeed in achieving our moral obligations.
The good news is that we aren't alone. Any time a European gives me a hard time about the US not fulfilling its obligations I whip out a map and draw a massive circle around Africa, the Middle East, South America, China and the East Indies/Indochina. Then I ask them to show me in those circles where they have fulfilled their obligations. European Colonialism had probably the single most long lastingly negative effect on the world of any and all actions taken by nations through time.
In general I would argue that America does a far better job of trying to fill its obligations than Europe does, as Europe's obligations are so insurmountably vast that they could spend the rest of their days working full tilt to fix the areas they ruined and still never get close. Still though, the Belgians complicity in the Rawandan Genocide ultimately doesn't excuse our own impotent responses.
MORAL AUTHORITY
Alongside the moral obligations used as justifications to intercede is the belief in the Moral Authority of the US to do so . The logic is that since we have done so well as a country (founders of modern democracy, oldest substantial modern democracy, defenders of the 'free world' during the Cold War, and #1 in the world by GDP for decades) we have therefore shown that we know what we are doing, and people should trust us to do what is right.
This is often part of the justification that is used when talking about things like invading Iraq, invading Vietnam, supporting a coup, bombing another country out of wartime (Libya), or just crazy shit (Noriega, don't know what else to call that one.)
This belief in our moral authority is rooted partially in a massive misunderstanding of geography, history and its effect on the world stage that gave us the last 50 years of glory. The biggest factor in that is WW2. After WW2 we were pretty much the only house left on the block after the hurricane. Everyone else was struggling to rebuild the most basic industrial infrastructure, and the countries closest to the action were shell-shocked so damned bad that it set them back quite a bit. In Mario Kart terms, we hit a lightning bolt.
Because of this, we skyrocketed ahead with ease. This is why we were the big dog in the Cold War. I doubt that Germany, France, etc, didn't want to be involved as much as we were, they simply couldn't be. This is also a big part of why we became so damned rich as a country. Capitalism The Game (TM) is pretty easy when you're playing a one person game.
But this isn't teh only cause of our success. Go back farther. If you think the American Civil War was bad (and it was, no doubt) it pales in comparison to the combined effects of things like the Spanish or French Revolution or the Napoleonic Wars when it comes to a developing country. Europe is like a locked diving bell with 5 dudes in it. When someone farts everyone suffers. Consider the fact that people were immigrating to the US in record waves, knowing they would be going straight into war, just so they could get out of there.
This is where geography comes in. So much of our success, ultimately, is simply a matter of geography. Our isolation gives us a massive advantage when shit hits the fan.
Because of this, our proclaimed moral authority isn't as strong as it sounds. On the other hand, it isn't all bad. We went to the moon. We did that. We built some of the most incredible industrial projects in the world. We did that. We are where the Silicon Revolution came from. We did that.
We have done great things, and because of that we may be able to do more great things for others. But we simply must be careful about what glories of our past we quote as justification. Our importance and success in the Cold War may not be apt justification for our involvement in the Middle East. Our ability to rebuild Germany and Japan doesn't mean we can do it in Iraq or Afghanistan.
-----------------------------
More to come later. I'll be honest, I have very VERY mixed feelings about this question. I do think we have a responsibility, even militarilly, but the justification for intervention is SO important.
