What are some examples of international incidents since World War II where America has taken on a policing role?

The United States military has taken a "policing" role in several conflicts since World War II. When the United States intervened in the Korean War, President Truman stated that "We are not at war" and that it was only a "police action." The reason Truman--and other presidents--have used the term "police action" to describe military conflicts is that it allows them to send U.S. troops into a conflict zone without a formal declaration of war, which would require approval from Congress. Since the Vietnam War was also never formally declared, many people refer to it as a police action, too.
The United States military has taken on more conventional policing roles, however. For instance, President Eisenhower occupied territory in Lebanon for three months during the 1958 Lebanon Crisis while the country experienced political and religious turmoil.