What actions by the Unites States (since WWII) in the international arena have generated the most controversy and why?

The triumph of the Allied Forces in World War II resulted in the United States rising to become a global economic superpower. Let's examine some of the more controversial foreign policies enacted by the United States in the last seventy years:

- The Bay of Pigs Invasion of 1961.

This failed military invasion involved a counter-revolutionary military of Cuban exiles trained by the Central Intelligence Agency being sent into Cuba with the objective of overthrowing Fidel Castro's communist government. With only half the forces projected as necessary for this operation present and JFK making the decision not to provide additional air cover, the forces were defeated and the opposite of intended happened: Fidel Castro became a national hero. This misstep also led directly to the Cuban Missile Crisis.

- The Somalia Intervention of 1992

President George H.W. Bush sent 28,000 American troops to East Africa to purportedly help resolve the issue of Somalian starvation, an effort expanded by President Bill Clinton. Tribesmen ambushed these troops, resulting in eighteen American deaths and many injuries. This move was controversial because there was no reasonable national interest present for the move—only the alleged "responsibility to protect."

- The Vietnam War

Out of fear of expansion of Communist empires, the US involved itself in this war between the Viet Cong and the South Vietnamese. The US interference here was largely viewed as meddling; the controversy was worsened by the fact that poor African American populations were dramatically impacted, the US employment of toxic chemicals (like Napalm and Agent Orange), and the grave toll on civilians.

- The carpet-bombing of North Korea during the Korean War.

Although President Truman's decision to enter the United States into the Korean War was overwhelmingly supported by both Congress and public opinion, controversy over this move eventually did arise much later, with accusations that the US had committed war crimes in North Korea. Because it was never covered expansively by the American press, what did ensue is sometimes referred to as "the most forgotten part of a forgotten war." The Atlantic expertly describes how the Air Force sent B-29s to bomb and napalm cities and villages across North Korea:

The bombing was long, leisurely and merciless, even by the assessment of America's own leaders. "Over a period of three years or so, we killed off—what—20 percent of the population," Air Force Gen. Curtis LeMay, head of the Strategic Air Command during the Korean War, told the Office of Air Force History in 1984. Dean Rusk, a supporter of the war and later secretary of state, said the United States bombed "everything that moved in North Korea, every brick standing on top of another." After running low on urban targets, U.S. bombers destroyed hydroelectric irrigation dams in the later stages of the war, flooding farmland and destroying crops.

This was largely considered—at least to the outside world—racist and unjustified violence against North Korean civilians. 

- The Invasion of Iraq

This move was predicated on the notion that the U.S. was fighting back against the terrorist forces responsible for 9/11, and yet Saddam Hussein did not possess weapons of mass destruction, nor was he majorly connections to the terrorists which perpetrated 9/11. The result of this invasion was chaos, from the beginning of the Arab Spring to the birth of the Islamic State.