The United States has by far the biggest defense budget in the world and it is the most active military power worldwide. In total, the United States has close to 200,000 active military personnel stationed abroad. Most are based in countries America has been at war with during the second World War, like Japan and Germany.
South Korea hosts the third biggest overseas deployment of U.S. soldiers, stationed there ever since the never officially concluded Korean War in the early 1950. Of course current military engagements also show in this infographic, like Afghanistan and Iraq. Check out the DoD's personnel statistics here.