Hurt-Comfort Fic

"And nothing makes us identify - feel with - another person as immediately as empathy for their pain. It's instinctive. It's the root for the highest of human virtues - compassion - and the lowest of human evils - sadism. In HC, one can shade into another and it's okay because no real people are being hurt during the filming of this fanfic."

—Hurt/Comfort: a Confession and a Celebration

A Fanfic about comforting one who is hurt. Usually based on either Break The Stoic or Break the Cutie, often to the point of Woobiefication: a regular character is damaged, either emotionally or physically, and another character (usually the character's partner, love interest, a teammate, or a Mary Sue) must comfort them. This comfort can become...intense. Alternatively, the author can create a Sympathetic Sue to get damaged so the author's favorite canon character can comfort him/her. A story can take place after specific episodes or installments of canon, or else the writer creates a new predicament. (The real trouble arises when they're not very novel about it, or pick a sensational situation that doesn't really fit the mood of the original series.)

Conversely, the above methods are often used by fanfiction authors as a way to force together two characters that would otherwise be at each others' throats or have nothing to do with one another. Maybe the characters don't know each other too well, or maybe they wouldn't get along well under normal circumstances, but once they see that poor kid bleeding on their doorstep there isn't much alternative to taking them in and nurturing them back to health....

Often used as part of Shipping. Sometimes, Ron the Death Eater is responsible for the "hurt" part and Draco in Leather Pants is responsible for the "comfort" part. (In fact, the derivation implied by those Trope Namers is quite common, typically with Hermione on the receiving end.) At other times, the characters stick to canonical roles (if not canonical characterization). In cases of physical hurt, it may be accidental or deliberately inflicted, but almost always there's some thinly-veiled reason why the injured cannot be taken to get medical attention (at least at first), which would involve them being cared for by mere strangers (with medical training) rather than someone who cares.

Fanwriters love this device because it gives the characters a situation which they both must struggle to overcome, without the author having to think too hard to create a believable plot. These types of fanfics will often be riddled with fluff and overly dramatized scenes in which the injured character lays out their entire tragic past for their rescuer to sympathize with (since Most Fanfic Writers Are Girls, part of this might appeal to women's tendency to value emotion and vulnerability), and more often than not transforms the characters' relationship from strained to romantic without much explanation in the interim, regardless of either character's gender or preference.

Can occasionally be done well, if the affliction is realistic and the story is well-written. Done especially often in medical show fandoms and buddy shows.

Often effective when combined with the Morality Pet, but ineffective when combined with Wimpification.

Common setups:

Rape.
Parental Abandonment
Heartwarming Orphan
Giving a character wings.
Comforting the Widow
Drug withdrawal. Unlike most of the above, it's overwhelmingly written as platonic or just open to interpretation - probably because the sufferer would be severely ill-equipped for typical romance (and the whole "needing a substance so much that it makes you violent towards your own True Companions" part). Almost always leads to Sleep Cute (or My God, What Have I Done?) situations after the worst of the symptoms leave.
Abusive Parents
Abusive relationships
Cold-Blooded Torture
Mind Rape
No-Holds-Barred Beatdown

Examples of Hurt-Comfort Fic include:

Bartending 101, a The Legend of Zelda: Twilight Princess fic, focuses on Telma the bartender comforting Link after the events and ending of the game.
Tails Returns: Cosmo is hurt and Tails is the healer.
Memories That Haunt, a Firefly Maliver fic. Warning, lemon, rape (as drama), and angst. Good fic if you like Maliver fics.
Chapter 15 of the Virgin New Adventures novel Set Piece by Kate Orman is actually called "Hurt/Comfort". In fact most of Orman's Doctor Who novels have at least one chapter like this.
- As is Chapter 5 of Human Nature.
95% of the Chris corner of the Charmed fandom consists of little more than rotruting the ever living daylights out of the poor witch.
The "Springsteen Trilogy" by Ars Longa is a Star Wars example. Callista just left Luke and Kyp heals him. But Kyp was molested on Kessel so now he's bi and Luke is the healer. It just gets weirder from there.
This trope is what makes all Shinji/Asuka shipping from Neon Genesis Evangelion possible since Shinji is too cowardly to make advances while Asuka hates his guts with a passion (plus she's afraid of getting too close to someone in the first place). Results may vary from WAFF to Nightmare Fuel, depending on the writer.
This fancomic for the Sherlock Holmes movie. Notable because both characters know perfectly well that they're in a Hurt/Comfort fanfic. Holmes isn't too pleased about always having to be the sick one.
Yellow Submarine is a Harry Potter Hurt/Comfort fic.
- In an interesting variant, not only does the rescuer immediately find the rescued a doctor rather than trying to physically heal her himself, the story only really starts years later, as they both begin to heal the emotional wounds of the other.
Many Star Trek fics involve Spock being comforted by his lover (usually either Uhura or Kirk) over the destruction of his home planet. Just as many involve Kirk being comforted by his lover (either Spock, or McCoy, or Uhura, or insert-literally-any-character-here) over some horrible event in his past, usually child abuse, Rape as Backstory, Tarsus IV, his troubled youth years, etc. Chekhov tends to be tortured and comforted later by Sulu a lot, too.
A lot of Film Brain fic falls under this category, mostly helped on by his Break the Cutie arc in Kickassia. As an interesting contrast, the other main woobie of the fandom is usually left broken.
The Ace Attorney fandom is a hurt/comfort goldmine, in part because the "hurt" part is as easy as trapping Edgeworth in an elevator or earthquake. One popular example of the genre is a (clean) Kink Meme fill called Sleepless.
There's a recurring Hurt Comfort Fic plot in the Carly/Freddie fic fandom in iCarly, that involves having Freddie hooked up with Sam, then playing Sam's violent and abusive tendencies from the show straight, without any of the Rule of Funny that it has on the show itself. An example can be found here: Candles.
You cannot throw a rock in the Buffy or Angel fanfic communities without bouncing it off at least three of these fics before it hits the ground. Of course, that's because the canon makes it so easy to write them. Joss has already more than taken care of the hurting for you, but its left up to the fandom to add the comfort.
Rent has Hurt Comfort Fic that's practically built in, with about half the cast having AIDS and Roger being a recovering drug addict on top of having HIV.
Kurt from Glee is tailor-made for this, being an out-and-proud Camp Gay who was bullied severely for it, especially by Karofsky who was revealed to be an Armored Closet Gay himself. Blaine is by far the comforter in the romantic fics, while Finn is the comforter in platonic fics.
My Little Pony: Friendship Is Magic has a lot of this type of fic. Out in the Cold and Kindness's Reward both revolve around one of the mane six (Twilight Sparkle and Fluttershy, respectively) finding, taking in, and falling in love with The Great and Powerful Trixie, humbled and suffering after the events of "Boast Busters".
- There's also a number of fics in which Rainbow Dash pushes her flight training too far and injures her wings, either threatening or outright dashing her dream of joining the Wonderbolts. "Rainbow Dash breaks her wings" fics became so ubiquitous that they were eventually banned on Equestria Daily.
  - Arguably, the concept itself was Jossed- Dash does break her wing in one episode, but she is taken to a hospital instead of cared for by another, and her wing heals just fine.
- A Sight For Really Sore Eyes is a classically hurt/comfort fanfic: love, accident, guilt, comfort, and finally shipping.
An Evening at the Airport , a long Tintin fanfic has a scene of this between Tintin and Martine. However it is a more subtle version of this as it is pretty understated and Martine's problems are shown as being more existential than the result of some trauma.
This is a staple of the Supernatural fandom. Dean in particular gets beat up, guilt tripped, humiliated, has his many insecurities flaunted, is verbally abused, tortured, raped, etc., with alarming frequency. The other characters are in no way protected from this though.
In The Adventures Of Blinky Bill, Shifty Dingo and Nutsy already have a strong hurt/comfort type of friendship in the canon, with Shifty usually being the hurt one and Nutsy being the comforter. In the Mother's Day episode, Shifty helped reunite Nutsy with her long lost father. In the Wedding Picnic episode, the children started bullying Shifty after Marcia bit him, causing him to cry so Nutsy put her arm around him as she led him into class. In the Apple Thieves episode of season 2, Shifty is accused of stealing apples and starts crying so Nutsy hugs Shifty and lets him cry on her shoulder. The fanfic Scars Are Forever by Canzet Yote takes this trope Up to Eleven when Shifty gets tortured and Nutsy stays by his bedside while he's in a coma and later in the same fic, his big brother Danny commits suicide. Cue Shifty crying niagra falls and Nutsy cuddling him.
This Axis Powers Hetalia fanfic. England visits America's house a few days after 9/11.
Force Of Good, a Tomb Raider fanfic that has Lara visited by an angel-like being after the death of her mother in Legend.
In the Dark a crossover with the Backstreet Boys and Spice Girls has a bus accident, survival and recovery.
Astral Journey: It's Complicated had Emma, who the narrator, getting badly injured in a freak accident and develop ESP powers.
Case of The Missing Technology has Melanie Jayne being kidnapped and a hacker finds the truth.
The infamous Girls Scream Aloud doesn't hold back, which got the writer in legal trouble. It was that bad.