America’s generals spend most of their time worrying about strong countries — understandably so. But for the foreseeable future, the United States has even more to fear from weak countries. In today’s world, it is only a matter of time (and often not a lot of it) before the consequences of weakness in the remotest areas become global.

Take China. There is much talk about how it might use its growing strength in Asia and beyond. Perhaps, but it has a long way to go. Meanwhile, a weaker China, characterized by slower growth and heightened unrest, is far likelier to embrace nationalism and turn to foreign adventure to distract a frustrated populace.

A different set of challenges stems from truly weak countries, those unable to meet their responsibilities to other countries and to their own citizens and that, as a result, pose a threat to both. Countries unable to control what goes on inside their borders are magnets for terrorists, drug cartels, pirates, human traffickers, and other criminal enterprises. A partial list includes Yemen, Somalia, Lebanon, Libya, Nigeria, Pakistan, Mali, Nicaragua, Haiti, Central African Republic, Mauritania, and Afghanistan.

Mexico is in much better shape than these countries, and, unlike them, is in no danger of failing. But state capacity is limited, and it will take a decade or more for authorities to strengthen police forces and develop a judicial system robust enough to deal with well-armed drug cartels.

Weak states pose a danger to everyone. Indonesia and Brazil are not always able to prevent the deforestation of significant areas of their respective countries, thereby exacerbating climate change. Indonesia cannot police rural areas adequately to maintain health standards, the result being the emergence of dangerous forms of influenza in farm animals that are carried through them to the human population in that country and beyond.

Weak states also tend to make poor economic partners. It is difficult to justify investing in a country with regular violence. It is similarly unwise to become dependent on a link in a supply chain that cannot be counted on. Political turbulence, disease, and conflict add significantly to business risk.

The best option for the United States is prevention — to keep weak states from getting weaker or to shore up states that are already struggling. This involves providing economic aid to governments willing to adopt the political, economic, and social policies known to attract investment and generate economic growth. It may also require training, advising, and arming national or local police forces to deal with internal challenges and the country’s army or coast guard to deal with external threats. If this all sounds like “nation-building lite,” absent the large military footprint, it is. The good news is it will more than pay for itself.

Haass is president of the Council on Foreign Relations and author of Foreign Policy Begins at Home: The Case for Putting America’s House in Order, from which this essay is adapted.

This story is from the May 20, 2013 issue of Fortune.