The Penance

I have concluded the investigation laid before the Count's Court by Harra Czurik of the murder of her daughter Raina...I find Marra Mattulich guilty of this murder...For this unmitigated crime, the only proper sentence is death...but in light of her age and close relation to the next most injured party in the case, Harra Csurik, I choose to hold the actual execution of that sentance. Indefinitely...
But she shall be as dead before the law. All her property, even to the clothes on her back, now belongs to her daughter Harra, to dispose of as she will.
Further. She shall die without sacrifice. No one, not Harra nor any other, shall make a burning for her when she goes into the ground at last. As she murdered her future, so her future shall return only death to her spirit. She will die as the childless do, without rememberance...
Every breath you take from this moment on is by my mercy. Every bite of food you eat, by Harra's charity. By charity and mercy-such as you did not give-you shall live. Dead woman.
"Some mercy. Mutie lord." Her growl was low, weary, beaten.

"You get the point," he said through his teeth. He swept her a bow infinitely ironic, and turned his back on her. "I am the Voice of Count Vorkosigan. This concludes my speaking."

—The Mountains of Mourning

A trope in which a character does something to mark himself and/or inflicts pain upon himself in order to atone for a misdeed. There is also an involuntary version where the state or some other authority stigmatizes someone in this way. Compare with Embarrassing Tattoo whose serious versions have some overlap with this.

Cranked Up to Eleven, this trope becomes Redemption Equals Death.

Examples of The Penance include:

Anime and Manga

Darker than Black has an example of this with the Contractor Bertha - when a normal person, she was a chain smoker and her baby choked to death on some of her cigarettes she left lying around. In the series, Contractors are people with powers who have a Renumeration (something they need to do after using their powers). Hers is eating and regurgitating something, but as a constant reminder of her carelessness, she chooses to eat and regurgitate cigarettes.
Yu-Gi-Oh! 5D's has criminals given an electronic tag that takes the form of a face marking.
In Samurai Champloo, Mugen has blue bands tattooed around his wrists and ankles, indicating that he had served time in a prison colony on Ryukyu. In Edo-era Japan, when the show is set, prisoners were often given such tattoos. Possibly averted in that the tattoos themselves aren't shown as stigmatizing in any way, or indeed worthy of any mention. The warrant for escaping an execution by faking his own death, numerous former opponents bent on revenge, and his own habit of entering lethal combat with anyone, anywhere, however, is another story entirely.

Comic Books

In Astro City, The Confessor is a sort of Batman expy with clerical motifs who is a vampire and in life was a priest. He did something evil once and so as penance wears a crucifix even though as a vampire it causes him pain.
Marvel Comics' post-Civil War member of the Thunderbolts, named Penance, wears a suit made of spikes that charges his pain-based superpowers.
Occasionally done in The Beano and The Dandy in the 1950s-1980s with characters slippering (In these two comics it was common for an ending of a strip to involve the character being beaten on their behind with a slipper for their misdeeds) themselves instead of their parents or other authority figure doing it.

Film

In the movie The Mission, Captain Mendoza kills his brother in a sword duel, and realizes what he has done to so many Guarani natives. He spends the next 10 minutes climbing up a waterfall with 50 kg of heavy armor tied to his back. Father Gabriel watches him, decides he has atoned for his sins, and makes him a Jesuit missionary.

Literature

The Scarlet Letter was borne by the book's female lead, Hester Prynne, for her adulterous dalliance with Arthur Dimmesdale, who self-flagellates for his own sins.
Older Than Print: Several stories about Sir Gawain, one of the Knights of the Round Table, involve a version of this in which he wears some clothing or marks his shield as a mark of shame, and as a nice gesture, the other knights adopt the same marker. One version has him doing this after accidentally killing a woman and in the romance Sir Gawain and the Green Knight he does this to atone for cowardly behavior.
Another old example is in The Rime of the Ancient Mariner, where he wears the dead albatross around his neck and is compelled to tell his story in order to atone.
For a non-voluntary example, the Remade of Perdido Street Station and other books in that universe.
One L. M. Montgomery short story talks about a lighthearted young woman who believes that she has accidentally killed her responsible older sister by a drug overdose; the young woman spends fourteen years abstaining from all the things she loves (like music, parties, and the man she's in love with) and dedicates herself to as much hardship and work as she can, to do penance.
The book Atonement is this trope - Briony writes the book after she grows up to attempt to atone for her sins.
Silas in The Da Vinci Code repeatedly whips himself, wears a leg bracelet that's made of barbed wire that digs into his leg, and a whole bunch of other painful things to apparently atone for killing the people he kills over the course of the book. Subverted, as he's a bad guy.
Aes Sedai in The Wheel of Time series will assign themselves a Penance for transgressions of White Tower law or custom. This can range from performing menial tasks better suited to lower ranked Novices to corporal punishment a la spanking. Egwene manages to treat her capture by Elaida and subsequent attempts to break her spirit, thereby breaking the rebellion as a form of Penance.
In The Lord of the Rings, Smeagol/Gollumn was in his back story banished by his mother the tribal chieftainess, for using the ring's power to find people's secrets. That is partly meant to show how the ring acted upon different people's nature. With Boromir the ring tempted him with political ambition and perverted patriotism. Gandalf and Galadrial claim they would have been tempted by hubristic desire to fix the world. Smeagol was just given the power to be a petty blackmailer and when he was found out he was exiled.
Vorkosigan Saga: At one time Miles Vorkosigan sentenced an infanticide to have her property rights stripped away and be considered legally dead as an alternative to hanging. The book seems to have some pity for her as she was caught offguard by changing times, but nonetheless she clearly deserved it and it was necessary to give a sharp reminder that disabled people were not to be killed out of hand anymore.

Live Action TV

Torchwood. Twice in one episode. In the series 2 finale
- 1). Jack Harkness lets his brother Gray bury him alive for nearly two thousand years because he feels guilt over letting him fall into enemy hands as a child. He even mentions this trope by name in dialogue.
- 2). Jack's ex-partner John, who Gray made bury Jack, joins forces with Torchwood afterwards and subjugated himself to Gray's wrath again.
In one Deep Space Nine(The House of Quark I think) a Klingon is declared dishonorable by Gowron. When that happens several Klingons form a circle around him and ritually turn their backs.

Poetry

The Alfred Lord Tennyson poem "St. Simeon Stylites" goes into the mind of a Christian saint, Simeon Stylites, who sat on a high pillar for thirty-seven years to atone for his sins. Subverted, however, in that the poem more than implies that Simeon's gesture is founded out of pride just as much as out of guilt.

"Have mercy, mercy, wash away my sin."

Video Games

The Arbiter from Halo does this. After being held responsible for the destruction of the titular setting in the first game, he's branded with a mark of shame in the involuntary variety.

Real Life

Because Humans Are the Real Monsters, many Real Life societies have inflicted punishments such as branding, tattooing, severing of limbs, etc., all for the purpose of stigmatizing criminals. Some still do.