Usually appears in fiction (and real life) in the form of furiously whispered rumors. "I hear Alice and Bob don't even sleep in the same bed anymore." Mostly used to indicate a marriage that has hit the rocks for whatever reason - sometimes a particularly bad betrayal of a spouse, sometimes serial small betrayals, sometimes simply a marriage where the love has died over the years.
There are a few times where this trope can be in play for other reasons. Sometimes there are uncomfortable sleep issues involved (snoring, etc.) and one side will be banished from the bed. The trope will also occur with either a Citizenship Marriage or someone who has Settled for Gay, although in those cases this may be the default state of the marriage. In neither case does this trope suggest the romantic problems that it will under the more stereotypical circumstances. In one case because the romance is fine - it's just the sleeping patterns that are bad, and in the other because there wasn't supposed to be any romance to begin with. Another possibility is that one or both of the couple are having medical or other problems that interfere with having a sex life. In even rarer cases, the married couple may be asexuals who don't find the sexless nature of their marriage an issue in the first place.
Note that characters who are implied to have sex and simply aren't shown sleeping in the same bed for propriety reasons are covered under Sleeping Single, although nowadays, the default assumption tends to be that a couple that doesn't sleep in the same bed falls under this trope, unless sex between the two is explicitly mentioned on camera. However, for this wiki's purposes, the reverse holds - unless it's explicitly mentioned that it's a Sexless Marriage, it goes under Sleeping Single. If it's subverted, then there still needs to be an explicit mention somewhere in the work itself that the couple is thought to be in a Sexless Marriage.
If sex is not included in a marital relationship in order to demonstrate the purity of the love the couple has, or due to some other restriction such as a Self-Imposed Challenge, it should go under Chastity Couple.
Since we can't or at least shouldn't know, No Real Life Examples, Please!
In Vampire Game Ashley admits to never having slept with Leene, presumably because of her love for Yuujel. This has clearly changed by the epilogue, as they have a kid.
A tragic case for Lady Ramia, whose husband refused to have anything to do with her due to their relationship. As a result, all three of their sons are adopted. And Seileiz, the eldest, is The Unfavorite for being the king's bastard son - seeing living evidence that her husband was perfectly willing to sleep with OTHER woman has pissed Ramia off for decades.
As of 2002 in Baccano, Firo and Ennis take Twice Shy beyond humanly possible levels: they have lived under the same roof for seventy two years, have been married for about twenty of those, and still haven't gotten as far as second base.
In the French comic Blacksad, the second arc features the chief of police who's part of a white(-furred) supremacist group, about whom rumors of pedophilia abound, because of further rumors that he and his wife have never slept together. The former are false, but the latter are most definitely true: It's because she knows, but he doesn't, that he's actually her father; their marriage was part of an elaborate plan by the daughter to get revenge on him for the way he treated her black mother after he started buying into white supremacist rhetoric. In this case the romantic implications are brought up, but that was kind of the idea to begin with.
In Finally Harry suffered through five years of sexless marriage before asking for a divorce because Ginny was terrified of physical intimacy.
Mean Girls - one of the secrets that Gretchen lets slip about Regina is "her parents totally don't sleep in the same bed anymore".
In the movie Pleasantville, it was revealed before the main characters arrived in town, sex was a concept no one could understand. When the mother was told teenagers were having sex, she had to be given a talk from her teenage daughter about what it was.
At one point in the 1981 comedy The Incredible Shrinking Woman, her depressed-looking husband is shown sitting in bed reading a book titled "Marriage Without Sex".
Lloyd and Caroline from The Ref have had a sexless marriage for years, apparently.
Emperor Paul Muad'Dib and Princess Irulan in Dune, while Paul's "real" wife, Chani, is a Hot Consort who is his wife in everything but name. Of course, Paul and Irulan were never in love in the first place (at least on Paul's side) and they both knew that the marriage was purely political, not to mention that Paul knew that sleeping with her would just play into the Bene Gesserit's plans. Despite mostly ignoring her he does seem to at least somewhat care for her, and in Dune Messiahspares her when the details of the conspiracy she was involved in, in particular Chani's infertility due to Irulan feeding her contraceptives and later Death by Childbirth, come out into the open, and he has to talk Chani out of having Irulan killed with the rest of the conspirators. It seems that at the very least he values her as an adviser, and after he exiles himself Irulan refers to him with some affection and helps raise his children.
In Wizard and Glass from The Dark Tower series, mayor Thorin and his wife Olive stopped sleeping together a long time ago, as he began pursuing younger women.
In Carrie, Carrie's Christian fundamentalist parents wanted to have a marriage like this, because they believed that Sex Is Evil. Her father once couldn't resist the temptation, and raped her mother; that's how she was conceived.
In The Hunchback of Notre Dame, Esmeralda marries Pierre Gringoire only to save his life, and doesn't let him touch her. He accepts that pretty easily.
In Tobacco Road, Lov's wife Pearl refuses to sleep with him, and doesn't even let him touch her.
In The Mercy Room, the protagonist is in a completely sexless unromantic marriage. It's not that they don't like their spouse, it's just the protagonist simply never felt anything for them. Eventually the spouse commits suicide and the protagonist goes on rather unaffected.
Karl Oskar and Kristina in The Last Letter Home after it becomes clear that Kristina won't survive another pregnancy. It doesn't last for long however.
Scarlett in Gone with the Wind decides that she doesn't want any more children, and tells Rhett that their marriage should become this. It does...mostly. Melanie has a delivery go very badly, and is warned not to have more children; consequently, she and her husband sleep apart. We discover — tragically — that Melanie and Ashley weren't entirely sexless either.
In Philippa Gregory's Cousins' War series, the Duke of Bedford arranges one of these with the much younger Jacquetta of Luxembourg because he believes a young virgin girl can help him with his alchemical experiments. There's no Real Life evidence to suggest this, although their marriage was short and childless (and it certainly wasn't due to infertility on Jacquetta's part, as her second marriage produced fourteen children).
In Death series: Imitation In Death reveals that Pamela and Niles have this sort of marriage. They pretty much hate each other's guts. Here's the kicker... Pamela is an Ice Queen with a total Lack of Empathy who knows that her husband is the psychopath and a Serial Killer, as well as knowing that he rapes the nanny, using his wife's frigidness as an excuse. Pamela does not care, because at least it doesn't affect her own little world. To add to the heinousness of the situation, they have a kid, and while the kid hasn't been harmed, Pamela didn't even think about kid's safety and well-being once!
In Tales of Kolmar, Lanen's cousin offers one of these to her after her father dies; he's the one with the passion to run the horse farm, she's the one who inherited. Lanen is offended by this and hits him, then decides to turn the farm over to him, keep a share of the profits, and go adventuring.
In A.S. Byatt's Possession, the wife of Randolph Ash is terrified of sex and can't bring herself to sleep with her husband. He's actually pretty good about it, and though he later has an affair with the poetess Christabel La Motte (which makes up the crux of the book) he never considers leaving his wife, and ultimately tells her that they had a sucessful marriage since never once in all those years did they have an argument.
This is the premise of Julia Valerian’s relationship with her third husband in A Voice in the Wind—he is gay and has a live-in catamite, and she is using the marriage as a cover to carry on an affair with a gladiator. It is superficially beneficial to them both (although it backfires on Julia; her lover isn’t exactly thrilled to hear that she’s gotten married), but they hardly interact with one another at all.
Live Action TV
In Frasier, Niles and Maris don't even sleep in the same room.
In Kaamelott, Arthur hasn't touched Gueneviere since their wedding, which hasn't stopped him from sleeping with just about every other woman in the castle or his in-laws from repeatedly slipping them fertility potions.
Monk is a highly germophobic man, and it was implied that he didn't have sex with his wife, though they loved each other.
Note that later in the series he regrets never having children with her.
Also later in the series, when Monk is reunited with an old crush, he tells her that he was married and that they "went all the way." So it's probably a safe bet that they did it at least once.
Most likely, Basil and Sybil in Fawlty Towers. They sleep in separate beds, and once, when he kisses her on the cheek (to throw her off), she tells him not to. In "The Psychiatrist", Basil claims that they "go for a walk" together two or three times per week, but he's probably lying.
Trey and Charlotte from Sex and the City. Early in their marriage, it becomes apparent that Trey struggles with impotency, and they sleep in the same bed but don't do anything with it. Over time, their situation becomes more strained, particularly as the struggle shifts from Trey's impotency to Charlotte's infertility, and in the weeks before their separation, Trey moves to the guest room.
Also, Grace's mother tried to push Will and Grace themselves into this. When both of them try to explain why this won't work, she simply says that sex in a marriage will disappear anyway and, apart from that, they were perfect for each other.
Lindsay's nephew George Michael has a crush on their daughter Maeby, and is tantalized by the possibility that she may be adopted. He and Maeby accidentally got married, but never became an official couple.
Heavily implied between Salvatore Romano and his wife in Mad Men. In fact it appears that the two of them barely even speak.
Klinger and his first wife, Leverne, from M*A*S*H. Klinger marries his Toledo sweetheart while in Korea, and the divorce happened before Klinger has a chance to return.
Londo Mollari, the Centauri Ambassador to Babylon 5, has three loveless marriages. He purposefully left all three of them back on Homeworld when he went to Babylon 5, and no matter how bad things seem at the station the thought that the three are back home waiting for him makes him firmly want to stay there.
In How I Met Your Mother, this happened to Robin's boyfriend Don and his ex-wife, and they eventually got separate twin beds. He then found out she was cheating on him with her personal trainer. Lily and Marshall decided to get twin beds for themselves because they found it to be more comfortable, though they were still having sex, and went back to sleeping together at the end of the episode.
In A Little Night Music, Fredrik and Anne's marriage lasts for eleven months without being consummated, though they both consider attempting it.
In The Little Foxes, Regina has not let her husband sleep with her since ten years before the events of the play. She claimed that there was something medically wrong with her, and hated him for believing her lie.
Hard to say just how long it lasts, but definitely longer than it should: in Disgaea3, after Almaz and Sapphire get married, and part-way through the honeymoon, Almaz complains that he hasn't even had the opportunity to kiss his wife yet. Implied not to be because the couple is not in love, but probably because the husband is the universe's ultimate Butt Monkey.
Female!Hawke could have something like this in Dragon Age II if she romances Sebastian, who took a vow of chastity before meeting her.
After Carver mocks this aspect of his sister's "marriage", Hawke jokingly replies;
Hawke: Aww, would you feel better if I slept with him? Because I totally would. Right here.
In the episode "The Perfect Castaway", when Peter disappears at sea and declared dead, Lois and Brian get married but don't have sex (though he would really like to).
In an episode of The Simpsons when Milhouse's parents Kirk and Luann were still married, after purchasing some of Grandpa's tonic, Kirk remarks: "Tonight, we'll push the twin beds together." This may have been foreshadowing of the upcoming divorce storyline.
After Apu cheated on Manjula, they still slept in the same bed, but with considerable distance between them.