Admittedly this isn't my specialty, because I've focused much more on the particular use of this kind of unit within more regular engagements and maneuvers, but the most famous example that comes to mind is that of "Tarleton's quarter." Named after the actions of Colonel Banastre Tarleton at the Battle of Waxhaws (AKA the Battle of Waxhaw Creek or Buford's Massacre), this was what revolutionary Americans called situations in which victorious forces killed surrendering foes.

Tarleton was a British light horse commander and a trusted lieutenant of Cornwallis. In May 1780 his troop came upon roughly 400 unmounted Virignia Colonials under Colonel Abraham Buford. Tarleton was quite a capable commander and his superior troops quickly overwhelmed Buford's men. Buford attempted to surrender.

At this point accounts differ sharply. In Tarleton's papers, which he published after the war, he claims that while moving to accept the surrender, a Virginian shot his horse from under him. His men, so enraged, then proceeded to massacre the Virginians before officers could bring them under control. In the end 133 Virginians died and 150 were severely wounded while 5 British troops died and 12 were wounded.

Historians disagree as to the culpability Tarleton bares for the event, but revolutionaries certainly used it to justify atrocities of their own across the colonies. One American example (admittedly with nothing to do with Tarelton's quarter) occurred at Fort Grierson, named after its British commander, outside of Augusta Georgia. Colonel Elijah Clarke, assisting General Andrew Pickens and Colonel Henry Lee took Fort Grierson and proceeded to massacre Grierson and his men.

On a somewhat related note, both of these atrocities were committed by irregular forces. Or, if not irregular, certainly not regular. Most units at the time consisted of lines of troops walking abreast to maintain rank and order on a chaotic battlefield. Tarleton and Clarke's men (though Lee might be an even better example here) were much less organized. They heralded a new kind of formation that was much more responsive to changing battle conditions because each individual member had greater autonomy. These units themselves were quite controversial from the view of 18th century commentators. Though they were highly effective at whittling down and attriting opposing armies, there are reported atrocities committed against civilians, women in particular. Though these are mainly centered on the Hungarian Grenz in the late 1750's, Tarleton's unit was certainly criticized for the way they confiscated or commandeered food and horses. An interesting area of further study might be the propensity of these irregular forces to commit civilian crimes in comparison to larger, more ordered bodies of troops.

Sources:

Lee, Henry. The Revolutionary War Memoirs of General Henry Lee. Edited by Robert E. Lee. New York: Da Capo Press, 1998.

Tarleton, Banastre. A History of the Campaigns of 1780 and 1781, in the Southern Provinces of North America, London and Dublin. 1787

Ewald, Johann. Diary of the American War: A Hessian Journal. New Haven: Yale University Press, 1979.

Gates, David. The British Light Infantry Arm. Tiptree: Anchor Brendon Ltd., 1987.

I have an interesting one.

Today the use of bullets specifically designed to cause extra damage to human flesh is considered a war crime. And while a soft, lead musket ball practically classifies for that on its own it appears that some some soldiers still didn't think their bullets were hurting the enemy enough. This lead to multiple varieties of mutilated shot including bullets hammered into cylinders or other shapes in order to make them tumble upon impact and cause larger wounds as well as bullets with nails or other bits of sharp metal hammered into them. Possibly one of the most brutal were bullets cut into 2 or 4 conjoined sections which would split apart upon impact.

In 1777 General Howe wrote this to Washington, “My aid-de-camp will present to you a ball cut and fixed to the end of a nail, taken from a number of the same kind, found in the encampment quitted by your troops on the 15th inst. I do not make any comment upon such unwarrantable and malicious practices, being well assured that the contrivance has not come to your knowledge.”

And to his credit Washington responded, “Your aid-de-camp delivered to me the ball you mention, which was the first of the kind I ever saw or heard of. You may depend the contrivance is highly abhorred by me and every measure shall be taken to prevent so wicked and infamous a practice being adopted in this Army.”

Regardless of how much each general knew however, excavations at the Monmouth found that mutilated shot appeared to be widely used by both sides.

Hope this is allowed mods, if it's not feel free to delete it, but I'd like to add that atrocities against Indian populations by both sides should not be ignored, and I'd be interested to learn of any instances of that as well

Can somebody expand upon the use of Tarleton's quarter at the Battle of Kings Mountain? Apparently, American militia men shouted this in response to surrendering Tories during the fight.

Also, I was given the impression that the worst and most violent fighting occurred between Tories and American Patriots in small skirmishes, raids, or full scale battles. Essentially, the worst atrocities that occurred during the war happened to Americans (and native Americans) by other Americans. Is there any truth to this idea ?