While there are fewer than two hundred independent countries in the world, there are more than sixty additional territories that are under the control of another independent country.
There are several definitions of territory but for our purposes, we are concerned with the most common definition, presented above. Some countries consider certain internal divisions to be territories (such as Canada's three territories of Northwest Territories, Nunavut, and Yukon Territory or Australia's Australian Capital Territory and Northern Territory). Likewise, while Washington D.C. is not a state and effectively a territory, it is not an external territory and thus not counted as such.
Another definition of territory usually is found in conjunction with the word "disputed" or "occupied." Disputed territories and occupied territories refer to places where the jurisdiction of the place (which country owns the land) is not clear.
The criteria for a place being considered a territory are fairly simple, especially when compared to those of an independent country. A territory is simply a external piece of land claimed to be a subordinate location (in regards to the main country) that is not claimed by another country. If there is another claim, then the territory can be considered a disputed territory.
A territory will typically rely on its "mother country" for defense, police protection, courts, social services, economic controls and support, migration and import/export controls, and other features of an independent country.
With fourteen territories, the United States has more territories than any other country. The territories of the U.S. include: American Samoa, Baker Island, Guam, Howland Island, Jarvis Island, Johnston Atoll, Kingman Reef, Midway Islands, Navassa Island, Northern Mariana Islands, Palmyra Atoll, Puerto Rico, U.S. Virgin Islands, and Wake Island. The United Kingdom has twelve territories under its auspices.
The United States Department of State provides a nice listing of more than sixty territories along with the country that controls the territory.