The term "police action" is generally used to mean American military intervention in a conflict that does not follow a declaration of war by Congress. For this reason, basically every American military action since the Second World War has been a police action, though the most recent invasion of Iraq—aimed at a regime change—is not usually referred to in these terms.
The first such action was US intervention, under the auspices of the United Nations, in the Korean Conflict in 1950. Communist North Korea had invaded the South, and had nearly crushed the ruling regime before American-led UN forces invaded. The conflict, which included Chinese intervention as well, ended in a stalemate and the establishment of North and South Korea as two separate nations.
Another action was the Vietnam War, which resulted from the desire of the United States to stop the spread of communism from North Vietnam to the South. This "police action" lasted many years, and costed tens of thousands of American lives. Eventually, Vietnam was unified under communist rule.
Another incident in which the United States took on a policing role was the invasion of the small Caribbean island nation of Grenada in 1983. Grenada was ruled by a leftist leader, and President Ronald Reagan sent Marines to the island, ostensibly to protect American citizens who lived there. They ended up, however, essentially overthrowing the Grenadan government and establishing a pro-Western regime.