There’s hardly anywhere in the world that the United States doesn’t have a military presence.
Here’s a map of where active duty U.S. military personnel posted overseas in foreign countries as of June 30, 2014. The figures are from the Defense Manpower Data Center, Office of the Secretary of Defense.
It doesn’t include over 1.1 million military personnel stationed in the United States and its territories, and it doesn’t include 36,345 that are classified as “Undistributed”, a category that includes personnel serving in Afghanistan, Iraq, Kuwait, and South Korea, as any unknown/classified locations. Naval personnel at sea are presumably categorized as being stationed on U.S. territory, so aren’t included. It also doesn’t include military dependents, of which there are over 22,000 corresponding to these military personnel in foreign countries.1
In many cases, the military personnel may be attached to the U.S. embassy or other diplomatic post.
The largest deployment is in Japan, followed by Germany, Italy, then the United Kingdom. Here are the 25 largest.