No Romantic Resolution

It has always been a staple of stories to include a bit of romance. Stories are also generally fond of tying up the story so everything is neat at the end, except when they don't. Point A plus point B put together means that any romance set up in the story will generally be resolved one way or another with characters either hooking up, breaking apart, dying or just walking away from the situation entirely.

But sometimes it doesn't work out like that. Sometimes the story sets up a romantic arc that never quite seems to get wrapped up completely. There can be several reasons for this, of which the most well known is not wanting to upset the status quo. Sometimes the author just wants to leave things open ended, or the author feels that resolving the romance would in some fundamental way work against the moral of the story they're trying to tell. The author just hints that the relationship may be forming. The common point between all of these is that the romantic plot lines were temptingly laid out but never followed to their absolute confirmed conclusion.

Thus, there is No Romantic Resolution.

Supertrope of Maybe Ever After, which implies a positive ending: the couple doesn't actually hook up but are extremely likely to. Contrast Marry Them All, where the romance is resolved but without choosing a single winner.

Anime and Manga

 * In Waiting in the Summer, while Kaito and Ichika are implied to be together at the end (as evidenced by her in the student film wearing a jacket his sister brought back with her on her trip), Mio and Tetsuro haven't seemed to officially hook up yet. However, neither one of them seems to mind the status quo, and at the very least they're still hanging around with each other.
 * Sora no Otoshimono: In the anime, Tomoki has sexual tension going on with all of the female cast members, particularly Sohara and Ikaros. He even, yet the series opts for the first option and doesn't ever come to a romantic resolution. The trope is even lampshaded when Mikako tries to hold a Shotgun Wedding and force him to pick one of the four candidates, only for the attempted wedding to be crashed by yet another girl (a little sister this time). Later, Sohara indicates that she really doesn't mind the status quo continuing for a while longer.
 * In the Tokyo Mew Mew anime, Retasu's fate is left open-ended; while the guy that liked her went back to his home planet and the guy she likes is still around, there's no definitive love confession.
 * Kyou Kara Maou didn't provide any definite answers either, although if you want to ignore the Yaoi Guys aspect of it and just view it as a parody, that hardly matters. However, in this instance, Yuri's lack of a definite decision may be more to avoid the wrath of the fangirls than to avoid upsetting his harem...
 * Code Geass ends without definite resolution on the part of Lelouch.
 * In the Mega Man Star Force anime, Luna and Harp Note at one point try to make MegaMan choose between them. In the original Japanese anime at least, Subaru (Geo) says "We're all just friends, right?" with which the girls are seemingly satisfied.
 * To Heart 2: The Unwanted Harem is unresolved after thirteen episodes and four OVA episodes. Well, when you do have ten twelve women in your harem...
 * Ranma 1/2 ends with none of Ranma's relationship issues being resolved in the slightest (with the implication that the situation is going to persist for quite some time). This is largely due to the author not knowing how to plausibly bring the situation to closure.
 * Haruhi Suzumiya is currently in a Type 1 situation. All the girls explicitly and canonically want Kyon (though circumstances and Haruhi are keeping all the sexual tension unresolved for now), while Itsuki claims to be solely playing up the Ho Yay to keep Haruhi from warping him into actually being gay for Kyon (emphasis on "claims"). Also, there's a couple of yuri-laden sidebars in the harem (Haruhi/Mikuru and Yuki/Mikuru), just to complicate matters more. (Haruhi likes it complicated.)
 * The anime for Trigun ends with Meryl waiting for Vash to return to her. She loves him, but it isn't entirely clear how he feels about her..
 * It's implied that Vash sees Meryl as sort of an inspiration for him in the next to last episode. Sort of like a new Rem? Make of that what you will. So odds are even if he doesn't exactly return it, he definitely wants and needs her in his life.
 * The anime version of Kuragehime.
 * Mobile Suit Gundam 00 concludes without ever resolving Feldt's unrequited feeling for Setsuna. Which is especially odd considering how strongly the movie seemed to focus on it.
 * The director claims he was trying to make yet another point about the difficulties of communication with that, basically that Setsuna still had big-time intimacy issues, and did not know how to properly convey his feelings (whatever they were) for Feldt. Even his accepting a hug from her prior to the final battle was a massive step forward for him.
 * Mahou Sensei Negima ends up this way for the protagonist, with the last chapter ending with nothing for him but Ship Tease and sunken ships for the three most popular contenders: Asuna, Nodoka and Yue. It's implied lightly that he hasn't settled down with anyone as of yet judging by the behavior of Makie and some of the other girls.
 * The ending does confirm that he has feelings for someone. It just doesn't say who. Although Asuna was very surprised to hear who it was...
 * None of the girls in Infinite Stratos get to hook up with Ichika at the end of the anime, although Houki comes close twice, once at the end of episode 12 (which is ruined by the other 4 pissed off girls), and once again in the second half of the OVA (she confesses, but its muted out by some fireworks that go off at the same time, so he doesn't hear it, and is distracted by them).

Literature

 * Robin McKinley's Sunshine ends with the heroine showing romantic interest in both her long-term boyfriend and her new vampire love interest. There's really no clue which she'll pick.

Live Action TV

 * While wasn't the end of the entire series, Goren and Eames leaving Law and Order: Criminal Intent  is played like this (Word of God says it was left open so the Broken Base can just pick the one they prefer).
 * My Name Is Earl had the Randy/Catalina Unrequited Love Switcheroo never play out to a conclusion despite teasing it.
 * While Kaylee and Simon finally get together in the Big Damn Movie, Serenity, the UST between Mal and Inara remains unresolved.

Film

 * The Woods has this, Heather and Marcy far from getting a romantic resolution, receive no relationship resolution at all; not even a hug or a verbal acknowledgement of the others' existence.
 * Subverted in The Best Years of Our Lives. The romance between  brews and brews and brews for much of the entire 172-minute film (almost three whole hours), only coming to a resolution  . Absolutely gut-wrenching to a first-time viewer.
 * The ending of Mirror Mask shows Valentine's counterpart in the mundane world is indeed real and has him enter Helena's life, but what their relationship will be or if he knows anything about the other world is totally up for grabs.
 * Primal Fear seems to be setting up the defence lawyer with the prosecutor, and they do have romantic history, but they don't work it out by the end.

Theatre

 * The written text of Shakespeare's Measure for Measure contains no answer from Isabella in response to the Duke's proposal of marriage. Many theater companies choose to play this as a Maybe Ever After, but that's their own interpretation of the ending; other theater companies imply that she turns him down.

Visual Novels

 * Higurashi no Naku Koro ni does not resolve the Rena/Mion/Keiichi love triangle. Rena has more subtext, Mion has more text text and the story opts to maintain the idea of friendship being most important. This means that Keiichi is still oblivious.
 * In Shikkoku no Sharnoth, the relationship between M and Mary does not evolve into a romance despite some hints. Whether M is even still alive is debatable.
 * Little Busters has this in the Refrain route, unlocked after every other route has been completed. While up until this point the story has been leaning towards primary heroine Rin and nearly makes her the canon heroine even in Refrain, at the end the situation is actually left ambiguous with Rin asking Riki which, if any, of the girls he actually likes. She doesn't get an answer. Which is good, since in Little Busters EX one of the new routes takes place after the end of Refrain.

Video Games

 * All of the romances from Knights of the Old Republic 2. There are plenty of hints and other showings but the romances never really get off the ground. This is due to LucasArts's insistence on a very short deadline resulting in a lot of content getting cut.
 * In one route of Blaze Union, the Nessiah/Garlot/Siskier/Jenon love quadrangle winds up on hold when the issues that have been plaguing Aegina boil over and she takes center stage. (The other two routes, however, do each have some form of resolution.)