We'll the major war crime that got reported was obviously the my Lai massacre which was committed in 1968 which was the worst war crime ever committed by Americans in a war. I assume you do not know a great deal so I will give a quick summery of what happened. This is from the court martial of Lt Calley who was one of the officers on the ground. The witness was one of the men under his command and he had the following to say.

" Lieutenant Calley came out and said take care of these people. So we said, okay, so we stood there and watched them. He went away, then he came back and said, "I thought I told you to take care of these people. We said, "We are. He said, "I mean, kill them. I was a little stunned and I didn't know what to do. He said, "Come around this side. We'll get on line and we'll fire into them. I said, "No, I've got a grenade launcher. I'll watch the tree line. I stood behind them and they stood side by side. So they -- Calley and Meadlo -- got on line and fired directly into the people. There were bursts and single shots for two minutes. It was automatic. The people screamed and yelled and fell. I guess they tried to get up, too. They couldn't. That was it. They people were pretty well messed up. Lots of heads was shot off, pieces of heads and pieces of flesh flew off the sides and arms. They were all messed up. Meadlo fired a little bit and broke down. He was crying. He said he couldn't do any more. He couldn't kill anymore people. He couldn't fire into the people any more. He gave me his weapon into my hands. I said I wouldn't. "If they're going to be killed, I'm not going to do it. Let Lieutenant Calley do it, I told him. So I gave Meadlo back his weapon. At that time there was only a few kids still alive Lieutenant Calley killed them one-by-one. The I saw a group of five women and six kids -- eleven in all -- going to a tree line. "Get ‘em! Get ‘em! Kill ‘em! Calley told me. I waited until they got to the line and fired off four or five grenades. I don't know what happened.... "

This incident lead to a large investigation and Calley was found guilty of the murder of 22 men women and children. Now there was an attempt to cover this up but it was very quickly realised that it was impossible with basically an entire village killed. Numerous people were brought to trial for that act. The public reacted in two ways which can be seen here in a copy of an opinion poll taken after the trial in which 78% of people did not agree that Calley should have been sentenced to life imprisonment. Now keep in mind that this is broken up because many people thought that Calley was a scape goat and they would disagree whilst others thought that he was innocent. Now there is a lot more that you can read about that massacre. Here is a website that has a lot of the primary sources on the trial.

http://law2.umkc.edu/faculty/projects/ftrials/mylai/mylai.htm

The standard example is the My Lai massacre, but as others have noted, it was far from an isolated incident. "Dr. Alje Vennema, director of a Canadian hospital near the site of the massacre, reports that he knew of it at once but did nothing because it was not at all out of the ordinary ... Colonel Oran Henderson, the highest ranking officer to have faced court martial for the My Lai massacre, states that "every unit of brigade size has its Mylai hidden some place," though "every unit doesn't have a Ridenhour", the man who spurred the investigation of the massacre.[1]

To take a couple of examples, one "former helicopter gunner ... told reporter Joseph Lelyveld that his gunship was ordered to halt a flight of peasants. When the pilot reported that he had no way to do so, he received orders to "shoot them". Thirty or forty unarmed villagers were then killed by the gunship." In another case, one soldier wrote to Preisdent Nixon "about his own involvement in an incident in which six gunships attacked a village, killing 350 villagers".[2]

Furthermore, these type of atrocities were apparently routine; according to Edward Opton, "I have personally accompanied a routine operation in which U.S. Cobra helicopters fired 20mm. cannons into the houses of a typical village in territory controlled by the National Liberation Front. They also shot the villagers who ran out of the houses. This was termed "prepping the area" by the American lietenant colonel who directed the operation. "We sort of shoot it up to see if anything moves," he explained, and he added by way of reassurance that this treatment was perfectly routine."[3]

In addition, we should consider the "deliberate policy of creating refugees where possible" as the NY Times' RW Apple described it.[4] He goes on: "An army general explained the idea to me as follows: ‘You’ve got to dry up the sea the guerrillas swim in—that’s the peasants and the best way to do that is to blast the hell out of their villages so they’ll come into our refugee camps. No villages,no guerrillas: simple".[5] This was carried out through "unrestricted air and artillery bombardments of peasant hamlets"[6] as well as defoliation, where "about one acre in six has been sprayed by defoliants".[7]

Finally, I haven't even touched on the Phoenix Program or the "supreme international crime" of initiating "a war of aggression", to borrow the words of the Nuremburg Tribunal.[8]

.

[1] Noam Chomsky, "The Use of Force in International Affairs", Yale Law Journal 80, no. 7, Jun 1971. Regarding Oran Henderson, see NY Times, May 25, 1971.

[2] Chomsky, ibid. Regarding the latter incident, he cites NY Times, April 26, 1972.

[3] Chomsky, ibid, citing Knoll and Mcfadden, War Crimes and the American Conscience.

[4] Chomsky, ibid, citing R.W. Apple, "Calley: The Real Guilt," New Statesman, April 2, 1971, 449.

[5] Kocher, Pepinsky, and Kalyvas, "Aerial Bombing and Counterinsurgency in the Vietnam War", American Journal of Political Science, 2011, citing the same article by Apple.

[6] Sheehan, "Should We Have a War Crimes Trial?" New York Review of Books, 1971.

[7] Chomsky, ibid. The wiki on Agent Orange may also be instructive, and contains two references for an even higher proportion of defoliation dispersal.

[8] http://www.roberthjackson.org/the-man/speeches-articles/speeches/speeches-related-to-robert-h-jackson/the-crime-of-waging-aggressive-war/

Michael Sallah and Mitch Weiss won the 2004 Pulitzer Prize for reporting on "Tiger Force," an anti-sniper platoon deployed in the "free fire zone" -- specifically, for reporting the first-hand confessions by soldiers from Tiger Force that the entire platoon participated in war crimes and did so on a regular basis. The details are pretty stomach-turning, basically rape, murder, and torture of women and children in hopes of blackmailing the men in that region into identifying the snipers who were attacking US forces and then hiding among the civilian population. The same article series and eventual book cites the task force's senior officer and his superiors as denying the whole thing. See Sallah & Weiss, Tiger Force: A True Story of Men and War.

(Not that this qualifies as a defense, but it's worth pointing out that those snipers were, themselves, violating the Geneva Conventions by participating in military action while wearing civilian clothes and by hiding among civilians. But it's unclear to what extent the Geneva Conventions apply to partisan forces resisting a military invasion; certainly no such cases have ever been prosecuted.)

US Special Operations troops and CIA field officers are also generally acknowledged to have participated in the kidnapping, torture, and execution of tens of thousands of suspected communist sympathizers, see any good source on the Phoenix Program. The official US line continues to be that neither the US Army nor the CIA knew that the victims of Phoenix were innocent civilians nor that they were tortured; no historian that I know of takes this claim seriously.

There is some very good discussion of the My Lai massacre, particularly with reference to the way it was justified in the minds of those involved, in The Scars of War (London, HarperCollins, 1993) by Hugh McManners, so I'd definitely recommend giving that a read.

See Nick Turse's recent book, Kill Anything That Moves. That should provide additional details and info.