Death Fic

A variety of fanfic in which the plotline is focused around the reactions of the cast to the death of one of their number. Frequently written in the first person, as the narrator goes on (sometimes at exasperating length) about everything they regret doing/not having done and everything that ever went wrong in their relationship to the deceased. Confessions of hidden love, secret friendship and occasionally responsibility for the death are common. Almost stereotypically ends with some variation on "Goodbye (name), life will never be the same without you/I'll miss you/I'm coming to join you just as soon as I open this vein."

This is a fanfic style which lends itself, predictably, to incredible amounts of Wangst at times.

Some Death Fics explicitly employ a Tomato Surprise by obscuring just who is narrating and/or who died until the very last moment. A few of these don't actually spring the surprise, instead forcing the reader to guess.

Not to be confused with a Dead Fic or Someone Has to Die.

Examples (sorted by original source media):

Anime and Manga

Ranma ½:
- Sent up hilariously in Gary Kleppe's Ranma Is Dead.
- Done perfectly straight by Reid Carson's Elegy For A Golden Youth.
Random1377's Neon Genesis Evangelion fic Aoi starts with Rei having to kill Shinji (perfectly justified under the circumstances) and spirals into the abyss from there.
The infamous Lucky Star Death Fic Ahoge by Zokusho.
For Descendants of Darkness, there's the fic When the Day is Bright. Unusually, this actually has a happy ending, which only adds to the feeling of catharsis after this fic has wrung you out completely.

Literature

The Harry Potter fic Perfect Situations by "Jeconais", one of the very first fics to ship Harry with Daphne Greengrass, is structured like this, with Daphne providing an unexpected eulogy at Harry's funeral. Subverted in that He's Just Hiding in a sportscar outside the church, and the two of them drive off together when she's done.

Film

Akallabêth is one for Inception that kills Arthur. Also features a very effective Downer Ending, even not counting the death.

Live-Action TV

There is, of course, this amazingly vindictive and far-too-detailed monstrosity about Barney the Dinosaur.
iCarly: One exponent is Lovely Amelie who has written several of these, including Castles In The Air, Up Into The Blue, and Days Like Masquerades.
One example of this in the BBC Sherlock fandom is a one-shot, Alone On the Water, told from John's POV as he watches Sherlock slowly die from terminal brain cancer.

Music

Tears of Loss by Beta_Mat_86 has Frida struggling with the death of her close friend, Agnetha. Olivia arrives to check up on Frida after hearing rumors about plans to reunite but has other ideas.
- Night of the Seance takes place during Frida's time in France and explains what got her to change her mind. The cause of the death of Agnetha, and her time in the afterlife are explained.
How Can It This Be has the Spice Girls checking out the games in Tokyo, Japan. Yet, they find out they weren't seen until Melanie tries to photobomb a couple. They learn the shocking reason they seem be ignore. They're actually dead and came back as ghosts to watch the games, with the families they were forced to leave behind.

Video Games

Go Not Gently kills off Vivi Ornitier in the prologue. His death shapes the entire plot from there on out.
A fic entitled The Many Deaths of Ms. Croft takes this to its logical conclusion for Tomb Raider. The fic essentially consists of a series of oneshots in which Lara Croft dies no less than 11 times in varying, but always gruesome, ways.
In the Katawa Shoujo fic Reconciliation, Hanako distances herself from Hisao and Lilly out of guilt for eight years, until she gets a phone call informing her of Hisao's death.

Western Animation

Parodied (amongst other things) in the Kim Possible oneshot Not Another Death Fic. In a nutshell: The characters try to avoid turning the story into a Death Fic...by turning it into a Shipping fic. Hilarity Ensues.
The unusually dark My Little Pony: Friendship Is Magic fanfic Bittersweet had Pinkie Pie get diabetes, and going on one last sweet binge because she couldn't live with it. Rainbow Dash runs away because she can't deal with everything in Ponyville reminding her of Pinkie, while Rarity tries (unsuccessfully) to resurrect her.
Final Stand of Death has folks who weren't lucky on Celebrity Deathmatch, which is a Death Fic in itself.