How U.S. troops are used

From an Associated Press article today on the current tensions involving North Korea comes this sentence, "Washington, which keeps 28,500 troops in South Korea to protect the ally, insists the routine drills were planned before last Tuesday's attack."

The article described war games involving a U.S. super-carrier and a South Korea destroyer in the Yellow Sea.

How many U.S. troops are stationed around the world like these 28,000? Why would the United States station 28,000 troops in a foreign country? How many years have U.S. troops been there? Ever since the Korean War ended in 1953? In 57 years why hasn't the U.S. trained South Koreans to protect themselves and brought our soldiers home?

What would a world map look like, if all the positions of similarly-stationed U.S. troops were plotted?