A Crown of Stars: Rei cared for Shinji greatly. When Shinji, Asuka and the like returned to Earth and met Rei, she was NOT happy to learn that her brother and Asuka were together now, and she stated she would not tolerate it and she wanted to take care of him personally. And then it was Asuka the one was NOT happy and declared that Rei was not taking him away from her.
Ai Yori Aoshi Koi: Chapter 8 reveals that in the past, Kaoru's aunt Suzuno actually drugged and raped Kaoru's father to conceive a child as part of a plan to become the Hanabishi heir. Yeah, it's just as f'ed up as it sounds.
There seems to be no sign of incest in the original book, but that didn't stop the The Chronicles of Narnia fans. The most popular pairings are Peter/Susan and Edmund/Lucy, with Peter/Edmund and Edmund/Susan all very popular as well. "Blame the chemistry between the actors." As you can imagine, given the Christian origins of the stories, this is a large division for the fanbase.
Subverted in Doing It Right This Time: Shinji and Rei had some mutual attraction, but it never really ended up going anywhere what with Rei having No Social Skills and Shinji not being much better off. At some point during or after Instrumentality he figured out that Rei was a clone of his mother, something his father had neglected to mention for some reason. Except unbeknownst to everyone, Naoko Akagi had switched Yui Ikari's genetic material with her own. Shinji is still wondering whether this makes that time he accidentally saw her naked less awkward or even more so.
They're technically not siblings, but Roxas and Xion are the main pairings in The Old Life, Alive Again. Keep in mind that one is Sora's Nobody and the other one is his clone. The other Nobodies (except Axel, Larxene, and Demyx) naturally don't take kindly to this, as they believe Nobodies should be incapable of loving each other.
Once More with Feeling: Defied. Shinji has decided that he will romantically pursue Asuka and treat Rei like a sister this time around. He still has to remind himself that Rei is his half-sister sometimes, though, since despite loving her like a sibling, he still finds her physically attractive.
The One I Love Is: Although Shinji likes Asuka he also likes Rei (and both girls like back). However Rei does not want to tell him she is his mother's clone because she is afraid that it will kill any possibility of having a love relationship with him. Later Shinji learns about her origin but he does not care about it because she is still Rei.
Thousand Shinji: Rei was in love with Shinji even though she was his mother's clone. However Shinji regarded her like a sister and was in love with Asuka. Still when Rei revealed her genetic make-up to him and Shinji figured out her feelings he did not seem concerned about her origins. In fact he told: "If you wanted a threesome with me and Asuka why didn't you ask us?". After the Final Battle, Shinji claimed Rei, Asuka and Misato as his wives.
The most infamous and best voted and appreciated fan story in the fandom is In Fire, In Ice, in which Justin and Alex end up married.
Everything the Light Touches (a.k.a. The Lion King 2 1/2) is filled to the brim with incest as it is, but one notable example would be when it's (very casually) revealed that Kovu and Nala both had Scar as their father, making them half-siblings. In the middle of one of their sex scenes, no less. Of course, this only makes it even more titillating for them. Beyond that, there's multiple different scenes where Kovu "entertains" Vitani. Cue the squick.
Also squicky in the fact that the OC knew that Diego was her brother all along but still engaged in a semi-intimate relationship with him. Diego on the other hand didn't know until after The Reveal.
The Mortal Instruments by Cassandra Claire is Ron/Ginny. Weasleycest in general is used quite often within the Harry Potter fandom. (To be fair, there are many Weasleys in which to cest.)
This assumption is entirely based on the fact that Clare once wrote a Harry Potter fanfic, despite the fact that the series have practically nothing in common, except that they are both YA modern fantasy. Even if we go by the theory that Clary is Ginny (because they both have red hair, which apparently makes them exactly the same), her love interest (and the only person she has sex with) is generally assumed to be a literal Draco in Leather Pants (because they're both blonde), rather than Ron, meaning it wouldn't fit under this trope, regardless of whether it's a Harry Potter fanfic.
The Dark-aligned pureblood families are a popular target as well, and not without some justification; between the apparently quite small population of magic users in the UK and their obsession with eugenics and blood purity it's actually rather plausible.
The series in question that is actually the fanwork is The Draco Trilogy and, to my recollection, features no sibling incest but implications of cousin incest between the sons of Gryffindor and Slytherin. The Mortal Instruments is a (largely) original series that got actual publication but that does have brother/sister incest undertones: the main characters Clary and Jace, spend a long time believing they are siblings and deciding to go ahead with their relationship anyway (because they can't stay away from each other). This is later made incredibly creepy when Clary's actual brother turns up and expresses interest in her.
D.Gray-man fandom has a somewhat sizable following of Leescest shippers. That is, Lenalee Lee and her big brother Komui Lee. It certainly helps that Komui has quite the sister complex and freaks out every time he's jokingly told that Lenalee's getting married.
One of the threesomes in the Magical Girl Lyrical Nanoha fic A Day in the Life is Ginga and her adopted siblings Wendi and Nove. Genya ultimately ends the relationship by having Ginga reassigned, though, but the three of them say they will take the time to think about their feelings for one another.
Golden Sun Gag Battle, a 4koma doujinshi, has a joke with Ivan trying out his new Reveal power on Hama and Feizhi's clothes. To be fair, Gag Battle was published before The Lost Age outed Hama as Ivan's sister.
Since Dark Dawn's release, there have probably been more, as several new sets of siblings have made debuts.
Bart and Lisa get a lot of incest fics. One in particular had them fall in love, marry and have a daughter together, living under assumed names in another town.
The first Shipping Chart◊ shown on the My Little Pony: Friendship Is Magic fansite Equestria Daily recorded no less than five fics shipping Applejack with her brother Big Macintosh, and another five with the sister/sister pairing Celestia/Luna (Princest). And those are just the ones that made it past the EQD pre-readers.
Ed and Al are a surprisingly popular pairing in Fullmetal Alchemist fanfiction, likely because the 2003 anime really went to town with the Incest Subtext, intentionally or not. Ed and Al seem to be a little too obsessed with each other for it to be merely brotherly love.
From Gravity Falls, the Dipper and Mabel pairing (also known as Pinecest) is very popular, with several fanfictions having been written for the pairing.
In a side story of A Brief History of Equestria, one of Platinum's plans was almost derailed when it was revealed that one of the kitchen staff of the noblepony she was having done in was pregnant with the grandfoal of the Noble in question. However, said maid was also the secret daughter of another maid, with whom the nobleman had most certainly sired the younger maid with years ago, leading to this trope. It isn't known whether or not the two younger ponies knew this, or if one knew and the other didn't, but given nature of the Founding-Era Nobility in character and in marriage arrangements, that knowledge may or may not have had any effect on the matter.
Hivefled: The Grand Highblood and the Condesce produced their respective descendants together and have every intention of making them follow in their parents' footsteps; troll society has no concept of incest, but Gamzee is still not happy about it. He has, however, made flirtatious comments to the ghost of their half-sister, but considering his current trauma level nothing was intended to come of that.
One of the most popular pairings in the Frozen fandom is the sisters, Elsa and Anna. Though many writers create AUs in which the duo are not siblings, others choose to focus on how the sisters admit their affection for each other, struggle to deal with the associated taboos and how to present the issue to their kingdom (more than one fic involves the pair being forced to flee Arendelle, temporarily), and balance their royal duties with their sharply increasing sex lives. Usually the affections are mutual; a few fics, though, make it one-sided, creating heaping amounts of Angst in the process.
In The Once and Future King, the main character, Prince Aziru, is the product of incest between Zuko and Azula, who have plenty of Incest Subtext in the original show. Unlike most examples of Royal Inbreeding, the siblings are not married (instead on opposite sides of a civil war for the throne of the Fire Nation), and Azula only chose to have a child with Zuko so they would have pure, strong Royal Blood. Aziru, along with everyone else, doesn't know who his father is yet, and only sees Zuko as the Evil Uncle he has to kill.
It should be noted that it's very unclear whether the sex was consensual, on either side. We don't know anything about how willing Zuko was, and Azula never specifically says she chose to have a child with him.
Seemingly played straight but ultimately averted in the Kim Possible fic "Vacation From the Norm". In the first volume, Global Justice head Betty Director appears to have betrayed GJ and has seduced her brother Sheldon, aka Gemini, leader of the World Wide Evil Empire. In the sequel, it's revealed that Camille Leone was impersonating Betty Director and was the one sleeping with Gemini. The real Betty had gone underground, and was actually romantically involved with Agent Will Du.
Due to being co-dependant on each other, Sam Winchester and his older brother Dean get paired up with frequency in the Supernatural fandom. The ship has been lampshaded in the show numerous times.
Twilight in Friendship is Witchcraft is in love with her adopted brother, Francis. She ends up killing his fiancee and marrying him herself.
The Second Try: Discussed. After Third Impact, Shinji and Asuka are the only surviving humans. At one point they argue that, if they have children and let them repopulate the world, sibling incest would be a problem. Fortunately this becomes a non-issue.
The Truth reveals that Applejack and Big Macintosh are Apple Bloom's parents, and that they're really stepsiblings. They eventually marry, with another foal on the way.
Extremely common in The Loud House fanfics. Lincoln has been shipped with all 10 of his sisters at some point (yes; even baby Lily) and that's not counting stories where the sisters are involved with each other.