"Are any of the characters in love?" "Yes, they're in love...WITH ADVENTURE!"
Minor exceptions: Rayleigh and Shakky are referred to as a "cute married couple", but whether they're actually married or just close friends hasn't been made explicit. Usopp has a potential Love Interest, Kaya, waiting at home for him, but they hadn't yet reached the point of Official Couple when he left. Mr. 9 and Miss Monday were shown to have a kid in a cover page.
In an extreme example, Dragon Ball follows the lives of several characters who marry and start families, although we're not shown much of the courting period at all, however there was a pretty noticeable build-up to both Goku/Chi-Chi and Gohan/Videl. This mostly came out of the creator's fears that he was terrible at romance.
Naoki Urasawa's Monster is probably the only anime that can regularly feature a relationship/connections chart between its Loads and Loads of Characters without even one romantic relationship. Eva had a few minor ones (none of them ended well), there was an old man and woman in a town Tenma went through that were implied to have developed a relationship after he left, and Johan disguised as Nina seduced intel out of a young detective with pure romance in volume 11.
Gundam Wing was written with no romance in mind at all. In an interview, the director specifically stated that he considered the political and symbolic relationship between the show's two leads more important than any potential romance. Despite that, there are some rather obvious romantic overtones in the Duo/Hilde relationship, and Heero and Relena even actually do share a kiss in the only canonical manga spin-off. The most seriously built up romantic connection, in the sense that it would be really cruel to take these two apart, and they build an emotional link and seem to fit together and all that, is Trowa and Quatre. It doesn't have to be sexual, but it's sure as hell romantic.
Word of God: "There is no romance in Lucky Star." They go so far as to have a scene that sets up what looks like a love confession, and then it turns out the guy wanted to talk to Kagami so he could beg her Yatsuhashi doll off of her.
Nelvana's Cardcaptors dub managed to, amazingly, turn a romance-heavy anime into a No Hugging No Kissing series. This isn't just aboutthecontroversialstuff; even the most acceptable pairs (mainly Syaoran/Sakura) became devoid of romantic interest. This became particularly bad in the Sakura Cards arc, in which Syaoran's feelings towards Sakura sometimes got 50% of an episode. In the dub, all the romantic scenes are cut out and the dialogue is changed to some more generic subjects (fighting the forces of evil, etc). To fill in the minutes of lost footage, many flashbacks were added. For example, while Cardcaptor Sakura last episode is an intense, emotion-filled finale, Cardcaptors last episode is almost a Clip Show.
The author of the Slayers novels stated that there would be no romance (again, like Toriyama, because he felt like he'd be poor at writing it), and whatever comes about resembling romance is either Played for Laughs or unrequited (namely the relationsip between Luke and Millina). When the anime was made, however, Lina and Gourry were cemented as an Official Couple, even sharing a (not remembered) kiss, and there was plenty of Ship Tease for Amelia and Zelgadis, who were strictly friends in the novels. A few more couples were thrown in for good measure. Later on, Kanzaka admitted that he didn't plan it, but realized that the characters all fell in love on their own.
Like Slayers, the original novels for Record of Lodoss War keeps romance off the radar. There's more of it in the anime adaptations, but other than Deedlit's crush on Parn, most of it is kept low-key.
In the Pokémon anime it seems like the only couples allowed consist of minor characters. None of the main characters are in relationships, and the only one who seems to want to be is Brock. Although, since almost none of them have hit puberty yet, this kind of makes sense. However, in the original soundtrack, 2 B. A. Master, there is a love song which implies that Misty has very strong feelings for Ash.
The only display of romantic affection in Claymore has so far been the single kiss Clare gave to Raki just before leaving him for good. Everything else never goes beyond I Owe You My Life sentiment and Vitriolic Best Buds relationship, much to the frustration of the considerable Yuri Fandom of the series.
Despite how deep most of the relationships tend to run in Soul Eater - with Soul and Maka being the most canon example - according to Ohkubo in an interview he doesn't plan on taking any of them to a romantic level. Though he also tends to troll his fans so whether or not he's being honest is unsure, and the Ship Tease isn't helping.
The Lyrical Nanoha series has almost no romance onscreen, although quite a lot is implied. Aside from Nanoha's brother and his girlfriend, the only confirmed relationship is between Amy and Chrono, and these characters mostly vanish after the second season, and even when they were a part of the show nothing actually happens onscreen. There are several character pairs that have romantic overtones, but none of them are ever explicitly shown to be more than friendship.
Probably the reason Hunter × Hunter is a total sausagefest. Any women in the series are minor characters who don't stick around long. The two main characters are also prepubescent.
According to Word of God, Daily Lives of High School Boys isn't so much about romance than teenage boys (and some girls) doing things. In fact, the closest things to romance the series have are the Literature Girl and Emi's crushes towards Hidenori, and even then they are one-sided (and in the latter's case, it was even grounded by Surprise Incest).
The Adventures of Tintin has this in spades, no major characters have shown any interest in romance whatsoever. The only exception is Professor Calculus, who has an innocent crush on Bianca Castafiore. According to the book "Tintin: Herge & His Creation", Snowy would have been a female human and love interest for Tintin, but that idea was discarded.
To quote the summary of Advent Crossover Crisis directly; "Rated T for swearing and violence, but relax, there's no kissing!" Indeed, romance is effectively non-existent in the story - a single ship between two featured characters is alluded to in the vaguest possible terms, and the two members of same never actually meet.
Imperfect Metamorphosis spreads around oodles of Ship Tease, especially between Marisa and Alice, Kaguya and Mokou in a side story, and whatever is going on between Rumia and Rin Satsuki, but never makes any relationships or attractions explicit. Even Yuuka's depravations are only implied.
In the film adaptations of both The Da Vinci Code and Angels and Demons, the romantic subplots between Langdon and Sophie and between Langdon and Victoria are scrapped altogether (it was stated that this would make the film less realistic). Langdon does give Sophie a friendly peck on the forehead, but that's about it.
This is a film too bad to be good & too good to be so bad it’s good. DULL is the watchword, unless watching Richard Gere’s Shatnerian reactions to a phone ringing is your idea of edge-of-the-seat horror. That Mothman never makes an appearance would be fine if the film gave us something else, or kept a mystery worth keeping- but nada. & this is perhaps the only ‘action’ film I can recall where a gratuitous love story would have improved the tale. Laura Linney’s Connie is the only character developed to any emotional or deep extent, or which induces any concern. She radiates a down-home sensuality, yet John never makes a move, even after saving her. Not even a peck on the cheek. Loser!
In The Numbers Station, there is no romance between the male and female leads, who are a radio operator and a spook who have only recently met. The two operators on the other shift, however, are hugging and kissing at the very least, but this isn't their story.
H.P. Lovecraft's stories do not focus on even the slightest bits of romance or affection. Even when the protagonist mentions a wife, it is usually in a rather offhand manner. The story The Thing on the Doorstep involved a marriage as a plot point but it wasn't the marriage of the protagonist, but that of a friend. Even then, no acts of romantic affection between said friend and his love interest are ever described, and, said marriage was actually just a way for an Eldritch Abomination inhabiting the woman to keep the husband close at hand since said Eldritch Abomination wants to eventually take control of said husband's body. Even friendships are subject to this since Lovecraftian protagonists often describe friendships in a detached manner, Any mention of sexual activity in Lovecraft is not only off-screen, but depicted as grotesque and produces abominable things that should not be. (The Dunwich Horror,The Shadow Over Innsmouth)
R.L. Stine's Goosebumps books often assign the protagonist a best friend of the opposite sex. No one ever seems to address the topic of romance between the two; in fact, there's virtually no difference between male and female characters at all. Differences between the sexes are only important when the characters are teenagers, just as said differences tend to be in real life. This is most likely because the books are aimed at prepubescent kids, and he wants both genders to be able to relate to it. There is one aversion, "How I Learned To Fly," in which the male protagonist actively wants his relationship with his female friend to be romantic.
Daisy Miller: The 19th century European aristocracy strongly adhered to this rule. Americans did not so much, however, and Daisy refuses to change her ways and (literally) do as the Romans do when in Rome. She finally becomes an outcast among her fellow American tourists when she commits the unforgiveable crime of strolling down the street on the arms of two men!
Deliciously inverted in The Ambassadors.
Several novels by Isaac Asimov. Asimov himself openly acknowledged his (at least perceived) inability to write interpersonal relationships, let alone romance, and on several occasions lampooned himself for it. There are married couples in his books, but their relationship seldom plays a large role in the narrative. With the ironic exception of The Gods Themselves, written in part as a response to criticism that his books didn't have enough aliens or sex, which featured alien energy beings having the least titillating (to a human audience) threesomes in history. Which are absolutely essential to the plot.
Power Rangers had three on-screen kisses in seventeen years (all done by the same couple, Kimberly and Tommy), often taking Will They or Won't They? to painful levels. According to SPD executive producer Greg Aranowitz, higher ups demanded as-low-as-possible levels of romance in the series, since it's targeted at little boys (he only said that about SPD, naturally, but who knows what goes through the minds of Disney). According to Dan Ewing, a kiss between Dillon and Summer was scripted for "Belly of the Beast", but was vetoed (we got the closest thing to it instead).
The original series did have some romance here and there, but it was so rare, almost never involved main characters, when it did it rarely affected the plot, and was more often than not two characters arbitrarily smushed together. The Doctor himself didn't have any interest in romance and often mocked it altogether if it did come up, largely written as asexual (except for a clearly romantic subplot with a guest character in "The Aztecs", in a prime example of the series' Early-Installment Weirdness). This is one of the main complaints that older fans have with the new series, which focuses very heavily on romance and turned the Doctor into an outright Chick Magnet.
At one point (particularly in the Davison era), there was a No Hugging, No Kissing, No Touching (for example, a comforting hand on the shoulder was a no-no) between the Doctor and his female companions, to dispel the notion of "hanky-panky" going on in the TARDIS. There were a few exceptions, like when Nyssa leaves. She gives the Doctor akiss on the cheek.
This became a bit of a Chekhov's Gun in Moffat's run of the new series, since the Doctor still firmly believed that "no hanky-panky in the TARDIS" was still effective. He gave his companions bunk beds and everything. Amy and Rory didn't listen at all, and discovered that hanky-panky in the TARDIS while it's in the Time Vortex can result in some very unexpected side effects. The Doctor's face when he realises that they shagged in his TARDIS is absolutely priceless.
30 Rock was very clear about this: Liz Lemon and Jack Donaghy never got together. Never. Not once. (Although they were married for one episode, due to a technicality, for what it's worth.)
Big Finish Doctor Who has fun with this. There's no longer any radar to slip things by and they can get away with things the old series never could, but the cast are still aware there's some kind of rule preventing classic Doctors from getting too close to people. Five's awkwardness makes Turlough wonder how he managed to have grandchildren, Six convinces someone he's not the Doctor by passionately kissing a woman, and Seven showing interest in a woman is a warning sign he's been drugged. Eight, the first Doctor to break the trend, is a Chick Magnet with a lot of painful consequences.
Warhammer 40,000 and all of its spinoffs, including the role-playing games, tend to gloss over or completely avoid the subject of romance and love, bar that love and desire feed one of the Gods of Chaos. It's understandable, given the settings' all-encompassing emphasis on war and mayhem, but even in the books, offhand references at best are the rule, with exceptions few and far between. Said exceptions are either mild (Ciaphas Cain, where it's mostly implied) or to show why this trope is a good idea (Ravenor, where it all ends horribly).
Warhammer, likewise, gives virtually no attention to romance or romantic/sexual relationships, thanks to being focused almost entirely on warfare and battles. Such things are touched on briefly in a couple of the novels, but always in passing and never as a major plot device or focus. The game materials themselves leave the romantic status of most characters almost entirely unmentioned. Exceptions include the vampires Vlad and Isabella von Carstein (who are married and deeply devoted to each other), the High Elf Prince Tyrion (who is the consort of Alarielle the Everqueen, though the precise nature of their feelings are not mentioned), the Wood Elf King and Queen Orion and Ariel (likewise a couple, but left at that) and perhaps Malekith the Witch King (who is rumoured to be disturbingly and unnaturally close to his mother Morathi...).
An example of Executive Meddling. There were hints of romance in the early flash animations and online games, but these were decanonized when the Lego Company decided to eliminate romance on the grounds that the core demographic (5-12 year olds) would find it "icky." Greg Farshtey, the lead story writer for Bionicle, also refuses to explain how new beings come into existence. To paraphrase Farshtey:
And then one of the movies went ahead and had an Unholy Matrimony plot. Farshtey had to handwave that one as merely a kind of political alliance, the same way kings would have their children married to strengthen bonds between royal houses (which to be fair is very much Truth in Television).
The rule officially only existed within the Matoran Universe (story years 2001-2008) where No Biological Sex strictly applied. Outside that, romance does exist, but is only touched upon twice: In the final novel, Kiina confesses her feelings toward Mata Nui by hugging him, and riding away in tears... and she was a feisty Action Girl who barely displayed any deep emotions like this up to that point. The only other example was the marriage between Sahmad and his deceased wife, as part of Sahmad's backstory.
Betrayal at Krondor has no romance, Disregarding Owyn's crush on Gamina or references to James's one-night-stands. This is facilitated by all six of the main characters being male.
Obsidian Entertainment's later Neverwinter Nights 2, in comparison, avoids it almost completely (save for a single scene under the moon), and whatever sexuality-related themes are there are mostly played for laughs. The expansion pack to Neverwinter Nights 2 however does have one romantic option for the main character (based on his/her gender). It affects your stats in game.
The relationships in the Super Mario Bros. games seem entirely platonic, with Mario and Luigi only receiving kisses on the cheek for the reward to each rescue. Surprisingly, Luigi is asked about Mario and Peach's relationship in Super Paper Mario, and he admits that it is confusing but they seem to be just friends. Additionally, Super Mario RPG employed joke kisses (where Bowser and Booster could accidentally wind up kissing Mario on the cheek or each other on the lips while trying to steal a kiss from Peach). Aside from that, the series just teases potential pairings such as Luigi/Daisy and Yoshi/Birdo.
Freelancer makes it very clear that Trent and Juni start out as brothers at arms to end up as close friends, but nothing more.
Touhou has no romance whatsoever. Hell, only a literal handful of characters even have known family members.
Dynasty Warriors was pretty bad with this, despite the canon couples such as Liu Bei and Sun Shang Xiang, then Sima Zhao and Wang Yuanji, most notably on the latter, which has both of them act like close friends instead of being a couple, at least. The closest to averting this trope is Wu's ending on DW7, with Sun Quan carrying Lian Shi (both are an example similar to Zhao and Yuanji).
As mentioned in the anime, there's little romance in Pokémon other than implications and subtext.
Love and sex are never mentioned in Dark Souls. The only marriage ever mentioned is off screen and neither character involved is personally encountered. However, it's heavily implied through Ciaran's dialogue that she was in a relationship with the Knight Artorias, even going so far as to say this as she dies, should the player kill her:
Persona 4 Arena is a very odd example. In the original game, the Silent Protagonist could pick from one of several girls from optional Romance Sidequests. Since Arena is a direct sequel, story wise, whether or not the hero (now named Yu Narukami) entered into a relationship with a girl, or who the girl would be is never discussed in order to keep it open and prevent Ship-to-Ship Combat. It's merely hinted at by some characters that he is a Chick Magnet.
Unusually for a Tales Series game, Tales of Vesperia manages to play this trope straight, or the most part. No romance seems to develop between any of the characters. However, it's not without its Dirty Old Man trope, wherein Raven often hits on the female characters. Estelle seems clueless, Judith doesn't care, and Rita gets violent.
Free Spirit cartoonist Peter Paltridge has no plans to make Winnie Goodwin and Thomas Harper a couple. While the show that inspired the comic created romantic tension between them, Peter fears that hooking them up would require Winnie to out herself as a witch to Thomas. The pilots of both the show and the comic had Winnie clearly state that the terms of her staying with mortals forbid Thomas from finding out about her magical abilities.
The closest thing to romance in Invader Zim is Gretchen's implied crush on Dib, Tak's brief and incredibly violent "relationship" with Zim (motivated by revenge and SCIENCE!, respectively), and GIR's very obvious interest in Gaz.
The first two seasons of ReBoot, strangled mercilessly by Executive Meddling, made sure to ruthlessly stifle any impression that Bob and Dot were romantically linked, or were at all interested in each other in that way. Needless to say, once cut free, the creators quite happily rectified that.
Despite the many love songs and possible Incest Subtext in The Amazing Chan and the Chan Clan, the lives of Mr. Chan and his children were decidedly romance-free (on camera, anyway). The only romantic subplot ever was between the family dog and a one-episode canine character.
Averted in the High School AU film My Little Pony Equestria Girls, where the main character Twilight Sparkle develops a crush on Flash Sentry in the human world and his pony counterpart in Equestria. Word of God has stated that this romance is restricted to the film and will not be presented in the show.