Richard Gardiner, a PhD student in the Department of Political Science at Georgia State University, produced this nice map showing the seven inhabited territories over which the United States claims sovereignty around the world. Those inhabited territories are American Samoa, Guam, Midway Islands, Northern Mariana Islands, Puerto Rico, U.S. Virgin Islands, and Wake Islands. (The uninhabited territories, which are not depicted on this map, include Baker Island, Howland Island, Jarvis Island, Johnston Atoll, Kingman Reef, Navassa Island, and Palmyra Atoll.)
As John Oliver recently discussed on his show, a longstanding question has been over whether or not citizens of the inhabited U.S. territories ought to have the right to vote.