Aggretsuko: Haida and Retsuko. From the beginning, he is in love with her, but too shy to do anything, while she gets a new Love Interest almost every season, and while the two are teased, they're still not together.
In Assassination Classroom, It is never officially revealed if Nagisa and Kayano got together even after the epilogue.
The star of Kenichi: The Mightiest Disciple, for the love of God. He and Miu have been at it for almost 400 manga episodes now, and it doesn't look like it will be solved anytime soon...
In chapter 423, Miu and Kenichi have a fairly straight-forward conversation about their feelings for one another. While Kenichi doesn't say "I love you" out loud, he does promise Miu that he'll only say that phrase/ask her out when he becomes strong enough to protect her, to which Miu agrees by kissing him on the cheek. How much more strength Kenichi needs though is YMMV.
The final chapter of the manga shows pictures of Kenichi and Miu being married and they have a daughter.
Welcome to the N.H.K. has the complex relationship between Satou and the girl acting as his "saving angel", Misaki.
In Elemental Gelade, Coud and Ren have yet to enter into a real couple relationship. Coud wants it badly but is too shy to confess his feelings to her during their journey to Edel Garden, and Ren did not show any strong romantic feelings towards Coud (at least in the manga).
Same with Tofu and Kasumi, to a lesser extent (and mostly in the TV series).
Inuyasha: Rumiko Takahashi just loves this trope. Nothing is really resolved until the very end when Kagome marries Inuyasha and Sango marries Miroku. To be fair, Miroku and Sango officially declare their commitment to each other before the end, although this is still done very late in the series.
Most of the plot in Lovely Complex revolves around the question whether the Huge Schoolgirl female lead can get a hold of the shorter guy she's in love with.
Hagino and Mari in Blue Drop get into a complex love/hate-relationship which leads to a lot of drama for most of the series. When they finally do declare their love for each other, their happiness doesn't last long though.
Nagi and Eva was regarded as one for some time but it as it turns out it didn't have a chance from the start.
Negi and Asuna was regarded as one for a while, but for the most part, since Negima started as a harem series, many of Negi's potential love interests could fall under this trope.
Negi's friend/rival Kotaro seems to have something like that with his roommate Natsumi; since chapter 262 came around, it seems that Kotaro does indeed have feelings for her (though they still appear to be mostly brotherly). The epilogue confirms they got married.
This applies to Boys over Flowers in every adaption, mainly between Tsukushi and Tsukasa and Tsukushi and Rui. This is thanks largely to the huge difference in social class between Tsukushi and almost every possible love interest that shows his face — though Tsukasa's personality certainly doesn't help matters.
El Cazador de la Bruja appears to be the only series in Bee Train's "girls with guns"-trilogy where the two female leads wind up with each other in the end.
Noir also seems to end this way, but Koichi Mashimo tacked on an ending suggesting that wasn't real.
The series usually pays zero attention to its several inexplicably unresolved romances - until it suddenly does, and then it's all big speeches, heartfelt confessions and revelations. And then it goes right back to pretending they're not there again. Repeatedly.
Code Geass is full of this. The protagonist Lelouch is really popular with the ladies, even without anyone knowing that he's royalty, but he's too busy secretly leading a revolution to actively pursue romance. Nevertheless, he gets plenty of Will They Or Won't They with Shirley (a friend with a borderline-obsessive crush on him), Kallen (a Tsundere terrorist who would do anything for Lelouch's charismatic Zero persona), and C.C. (the Sugar-and-Ice Personality witch he made a deal with in exchange for power).
The basic premise of a girl wooing another girl into becoming her soeur also has something of this.
Ah! My Goddess can be seen as one long Will They Or Won't They between Keiichi and Belldandy, even though it's a foregone conclusion that they will be together in the end. The number of times they've kissed in over a hundred chapters can be counted on one or two hands! If you count in all the animated series, you'd only need to use fingers and toes to count. They get married in the final chapter of the manga.
Sunako and Kyohei from The Wallflower, to ridiculous heights. So far, they've risked their lives for/saved each other countless times, kissed twice, confirmed they don't hate each other, gone out on a date and lived together for a period of time. And, yet, what is there for them to say at the end of the day? "We aren't in a relationship." Ugh.
Shiki and Mikiya in The Garden of Sinners. He confesses to her early on, and is welcome to regularly drop in on Shiki, and its clear that Shiki feels something towards him, and yet in four years nothing happens; rather frustrating considering the lack of UST. Especially strange considering the games Nasu later came to be known for.
Pointed out in School Rumble Z when Yakumo visited Tenma in the US. When Yakumo still cannot define her relationship with Harima, a very frustrated Tenma threatens to crash the car she's driving.
The central question in Shoujo Sect is whether Shinobu will get a hold of her childhood friend Momoko. She does, but not before going through a harem of other girls.
Phantom Quest Corp. makes the UST between Ayaka and Detective Karino fairly obvious, to where she even flirts with him on occasion. But the series was cut short at only four episodes, so it ended before the issue could be resolved either way. So at most, theirs is a "Maybe".
Spice and Wolf: There are only two main characters. One of them is both a tease and a woobie. The other is a Nice Guy with a hint of snark. They spar with words all the time, but it's pretty clear that they deeply care about each other. It still counts, though, because of an important obstacle.
In Black Lagoon, Revy and Rock. They even share an Indirect Kiss (lighting a cigarette) in Chapter 9 of the manga and the equivalent anime episode.
Ghost in the Shell features this to a painful extent. While the tension is obvious in the movie adaptations, Stand Alone Complex takes it even father. Even the voice actors have been known to make jokes regarding the tension between them. And yet, no real resolution is ever reached, aside from a very faint Maybe Ever After in the end of Solid State Society. Batou puts him arm around her and she doesn't throw him into the pool
With the other two, there is the problem that Haruhi has already almost rewritten the universe out of jealousy earlier (but she doesn't know this), which is a problem right there. Also, Mikuru isn't allowed to have relationships with people from the past and Yuki seems like she cannot express emotions. And that is cannot in the same way that a blind person cannot see and a deaf person cannot hear. It seems she was not created with the capability.
In Nisekoi, Raku and Chitoge are both unable to admit any positive feelings they have for each other. Nearly every chapter either involves one of them (usually Chitoge) trying to get closer to the other or one of the side characters learning something significant about someone else. Of course, so far, there has been little progress—any attempt between Raku and Chitoge to do anything romantic that even makes it past the first step seems to involve the universe conspiring to keep their thoughts secret to each other, and side characters seem to like keeping information to themselves and thus have no bearing on anything.
Kagerou Project is full of these, some more obvious than others. Takane and Haruka both have confirmed feelings for each other but have a number ofhurtles in the way, with Shintarou and Ayano their feelings have been heavily hinted at but they also have some major road blocks, Seto and Mary are also heavily hinted at having deeper feelings, and Kido and Kano seem stuck in a never ending cycle of Slap-Slap-Kiss.
In The Hating Girl, this starts setting in fairly soon, and kicks into high gear about 3/4 of the way through the manga, with the sticking points being the constant misunderstandings between Asumi and Ryouji and Asumi's emotional turmoil about her self-worth. They finally become a couple after defeating the Mad Bomber and consummate the relationship in the last chapter.
Yuri!!! on Ice was full of constant Ship Tease between Yuri and his longtime idol and now coach, Victor, for the first seven episodes, with each one seeming to push the sexual tension ever further toward its breaking point. It finally broke at the end of episode 7, when Victor kisses Yuri and they become the Official Couple. As of episode 10, they're engaged.
My Wife is the Student Council President: In Izumi and Ui's case, it has nothing to do with whether they'll hook up. That's practically a given, if you haven't noticed the title. It's more a question of when will he finally screw her and just get it over with, since Ui has already given him the green light and she's just as horny as he is. The only reason they haven't done it yet is because their friends and neighbors won't let them.
Played straight for a while, and then subverted in My Monster Secret: The first half of the series runs on this between Youko and Asahi, but when they finally do spit it out, the series continues.
The series also contains several other cases of this, such as Aizawa for Asahi.
Skip Beat! is rife with slow-burn Ship Tease between Ren Tsuruga and Kyoko Mogami. It takes Ren about seven volumes to admit his feelings, Kyoko thirty-three volumes to admit hers, and forty-five volumes for either of them to do anything about it. This has become something of a meme within the fandom.
In the anime of Tales of Zestiria, while Rose and Alisha have a steady relationship buildup that isn't really present in the base game without the DLC (and that has a very different storyline), it only brings up Will They Or Won't They? Ship Tease at the end of the second season. Unfortunately like Sorey and Mikleo in the game (while they still have Ambiguously Gay implications in the anime, due to story changes and adjustments it's less obvious), the question is left hanging.