Tarring and feathering was a relatively common (though extralegal) punishment until recent times. Did the recipient usually suffer any permanent damage from burns, or was it more for the sake of humiliation?

Very rarely was there any serious physical damage done by the act of tarring & feathering itself. Sometimes the person being tarred & feathered had other humiliations heaped on him (such as being drug through town or beaten) that caused damage, but rarely was the damage permanent.

There are a few things about the act itself that should probably be cleared up to help with this question.

First of all, the tar being used was not the thick road tar or roof tar that we think of today when we think of tar. It was usually pine pitch, which heats at a much lower temperature than petroleum based tar. Thus it would cause much less damage to the skin when it was poured on.

Secondly, tarring & feathering was almost always done to a clothed person. There's a scene in HBO's John Adams which shows a man being stripped naked before being tarred & feathered. This is in accurate. Generally it was done with the man's shirtsleeves on, sometimes with even shirtsleeves & waistcoat.

Almost all cases of tarring & feathering were customs related, and generally done to low ranking members of society. Very rarely was anybody who was a high ranking member of society even threatened with tarring & feathering, much less having it carried out.

John Malcom is one of the most famous cases of tarring & feathering in colonial America, because it was one of the most brutal. In addition to the tarring & feathering he was forced to ride in a cart through town in the middle of winter. He was beaten with a stick, and had a knife held to this throat to make him swear that he would resign his post. He was even threatened with hanging a couple of times. All in all he spent four hours in the middle of a Boston winter without any warm clothing to protect him.

He recovered to full health, and when the Revolutionary War started he left for England. He kept a piece of his dried skin in a box as a memento, though at this point it's impossible to know whether it was the tarring that caused the skin to peel, or being beaten. (Part of what made his experience so bad was also being stripped to the waist--the crowd may have felt this step was necessary as Malcom had been tarred & feathered previously in another town before moving to Boston.)

The whole point of tarring & feathering was (as Gordon Woods points out) to bring the transgressor back into the societal norms. To quote Wood: "But always the aim was to get the suspected persons to recant their former ties to the crown and to reintegrate them back into the community"

Tarring & feathering as practiced in the Revolution actually began in the 17th century in port towns along the Atlantic with sailors regulating other sailors. It came with sailors in America and was mostly practiced by sailors in America to again regulate sailors & customs officials (most targets of the practice were sailors informing on smuggling or customs officials).

It's also an experience that wasn't practiced nearly as often as it seems. It looms large in American cultural memory as being completely tied to mob action, but various other forms of mob action were far more common than tarring & feathering. (It's also worth pointing out that tarring & feathering grew out of earlier traditions involving crowd discipline of those outside societal norms. These earlier traditions are sometimes called "rough music" because of the noise made by participants as they were shaming the targeted individuals.

Some sources:

1.) Radicalism of the American Revolution by Gordon S. Wood

2.) The Shoemaker and the Tea Party by Alfred Young It was Malcom's caning of Hewkes (the man who this book is about) that led to Malcolm's second ordeal.

3.) Bunker Hill: A City, A Siege, A Revolution by Nathaniel Philbrick

4.) “English Plebeian Culture and Eighteenth-Century American Radicalism” by Alfred Young in The Orgins of Anglo-American Radicalism