Globalization says it all. Many major world businesses are international and a poor economy in one part of the world will affect us here at home. Take the automobile industry for example. Honda, Toyota, Nissan, Acura, Isuzu, Subaru, and Mazda are Japanese automobile companies. Imagine if Japan was devastated because of a series of natural disasters or war and the United States or any other country didn't intervene before it was too late. Those brands would no longer exist eliminating a massive contributor to the international automobile industry and economy. All of the overseas manufacturing plants that are part of those companies would shut down (including the large Toyota plants that are located in the U.S.). International supply companies that helped supply those companies with raw materials would lose business and possibly go bankrupt depending on how reliant they were to those customers. It would cause a collapse of a large fraction of the world economy. This is only one example and a virtually unlimited scenarios that may have a larger or smaller impact. Oil industry is another great example.
We are also a globalized society human rights crises are almost always brought to light over mass media. Many humane groups, and rightfully so, demand somebody to help the victims. It is morally and humanly correct as a global society to to do something to help other people regardless of their nationality. Syria is a good example. Some human rights issues can be brought up not because of an oppressive government, but because the economy is just too poor to fill the demand for basic necessities. That is the reason for foreign aide.
Honestly, the United States does not even spend that much on foreign aide like some people seem to believe. Currently, the U.S. spends about 1.5% of the entire federal budget on "international affairs" that includes foreign aide.