Mazinger Z: Kouji and Sayaka were the couple defined Belligerent Sexual Tension. In spite of being attracted to each other, fierce competitiveness and pride issues on both sides prevent them from reaching an understanding and being together. It was not so bad in the original manga, though. And in another manga version, they kissed when they thought Kouji was going to die. He survived, but Kouji avoided Sayaka for a while because he was still too afraid and insecure.
The manga and anime have this in spades, diamonds, clubs, and especially hearts between Keiichi and Belldandy. They're not only the Official Couple, they practically live like a married couple, look like one to everyone else whenever they leave home, they have several 'shippers on deck, and it's obvious to viewers/readers they want a Relationship Upgrade. Then why hasn't their relationship moved past kindergarten-level? Not only is Keiichi is extremely shy, a law against physical relationships between goddesses and mortals puts a lock on some of his more physical urges. Also Belldandy has stated that she is not ready to fulfill his desires; not to mention she appears to be oblivious to all things sexual. Still, with all the heartwarming they've shared, resolving the tension seems like a Foregone Conclusion.
To illustrate her oblivious nature, when they were standing in front of a love motel in the rain and Keiichi was wondering whether to go in with her, Belldandy grabbed his hand, appearing to give him a signal that she was ready, turns out she just wanted to know if she should make the rain stop and was totally unaware of the love motel. And the only thing Keichii could bring himself to do when they went inside was ask the desk clerk if they could borrow an umbrella.
Code Geass. The shippers probably went ballistic over the romance of this series: three valid pairings for the male lead alone, and enough done by one side or the other to establish the attraction as canon. The relationship between the two Tsunderes, Kallen and Lelouch, was especially frustrating because practically all the moments they had were interrupted by a character or an event, that is until she stole a kiss from him near the end, only to get completely ignored by him, for a good reason.. The other two love interests were Shirleywho spent most of the series with a crush on Lelouch and then died one episode after Lelouch finally come to actually notice and acknowledge the girl's feelings and C.C.who spent most of the series helping Lelouch just so she could pass her curse of immortality onto him in the end and die. There was also that fact that shekissedhim a lot.
And there's Kaguya, who's certain that the Unresolved Sexual Tension between Zero and his Number Two and Red Queen has been resolved, as it were. ("We are Zero's three court ladies~!") She then plots to get in on the action, in-line with her actual romantic aspirations, and suspected dubious sexuality. Too bad she doesn't get that much screentime.
Haruhi Suzumiya series features this between Mikuru and Kyon, although this tends to depend on your camp and which theories you may subscribe to. Unfortunately for them, Haruhi isn't about to allow that come hell or high water due to her own UST with him (as exemplified by how Kyon saved the world from being remade by stealing a kiss from Haruhi, and the ending of Someday in the Rain), and on top of that it's also forbidden for Mikuru by time traveller-rules. Her future self tells him she's glad to see him again, which strongly implies that nothing ever came of it. If you believe Unreliable Narrator Kyon, he doesn't take future Mikuru's suggestion that he kiss her younger self while she's asleep. But considering that he's likely to get written out of existence if he upsets Haruhi, he's got ample reason to not tell anyone if he did.
Sango and Miroku. The UST is so obvious that their grope-slap exchange becomes a running gag throughout the series.
Inu-Yasha and Kagome have this in spades, although it often manifests as Belligerent Sexual Tension. This is even parodied in a Robot Chicken episode. Where the dad of the girl who was watching the series got really into it. When his daughter told him each episode only comes on every week, he states, "I'm not going to wait another week to see if Inu-Yasha and Kagome get together!" So he caught onto this after only watching a single half-hour episode.
A more one-sided example is that of Setsuna toward Konoka. This gets turned up to nine thousand for the Spring and Summer anime specials. It started to resolve from chapter 252 with an epic Pactio. Doesn't seem to be one-sided, either (Konoka was the aggressive one during the kiss).
Negi has some form of this with most of the primary female cast members.
Spike and Faye from Cowboy Bebop. Mostly one-sided, on Faye's part. Spike seems rather hung up on Julia. However, Watanabe once stated in an interview that "Spike may have feelings for Faye, he's just not one to outwardly express them." Considering the type of person Spike is, it makes sense.
Roy Mustang and Riza Hawkeye in Fullmetal Alchemist combine this with both Bodyguard Crush and Subordinate Excuse. It's especially present in the manga and the Brotherhood anime, which also feature increasing UST between Ed and Winry. The latter UST does eventually get a resolution. The Royai UST is actually acknowledged by Riza in-series and used for her own ends, very awesomely.Word of God in the third art book says that the series ended without them getting married because of the military's anti-fraternization law. The Chronicles book released in autumn 2011 does confirm that they remain side by side for pretty much the rest of their lives, though whether They Do ever happens is still left open for interpretation.
Godchild and Count Cain fall into this trope easily. Half of the series is Cain kicking some ass the other half is having angsty dialogue with manservant Riff about how they'll accompany each other to hell and other such lovely things. Despite all of this the manga-ka Kaori Yuki claims they weren't a couple in the Angel Sanctuary art book.
Vassalord IS this trope. Except it kind of gets resolved. Kind of. But not really as Charley and Johnny still haven't done it despite obviously WANTING to. Charley walks in on Johnny showering without a problem.
Hana-Kimi has a lot of this. We've got a girl disguisedas a boy rooming with a boy that knows she's a girl but she doesn't know he knows, and they both have crushes on each other. And then another boy has a crush on her, but doesn't know she's a girl. Tons of Will They or Won't They?. Plus, taking place at an all-boys Boarding School, there's a ton of Ho Yay between male side characters.
Sayonara, Zetsubou-Sensei also has a lot of this, essentially the upshot of every single girl in the class being in love with the teacher. He is almost pathologically resistant to their affections (ethical concerns aside), but is painfully aware of the UST, which is why he has stopped resisting Tsunetsuki's stalking as doing so only spurs her to more extreme behavior. The class exists in a kind of equilibrium where the UST never quite boils over, at least until somebody or something kicks over the anthill, such as Nozomu's arranged marriage in season 1, his flirtatious body-double in Zan, and an out-of-left-field love-confession from a random student in the same season.
In Princess Tutu, once Fakir finds out about Ahiru's secret there starts to be a lot of UST between the two, normally centered around Fakir accidentally being around when Ahiru turns from a duck into a (naked) girl. It doesn't help that another character repeatedly forces her to change in front of him on purpose.
Daisuke Moriyama's World Embryo, repeats Chrono Crusade's structure. Amane × Riku was interrupted by Amane's death. So now we have Rena × Riku (lampshaded massively due to them being "Mom" and "Dad" to Nene, potential kiss interrupted by Nene), Riku × Nene, Yui × Riku (averted), Yui × Takao (averted by death), Hayato × Suzu (come on, she helps him with going to the toilet and bathing...), Kota × Mizaki, etc.
Rito is practically made of this trope, towards Lala and Haruna especially. He'd had a crush on Haruna that was at least a year old by the start of the story, and all of there interaction is chock full of UST. It's little better with Lala, who he refuses to admit to even the possibility for 100 chapters.
Let's not even get started on the UST the girls have towards him either, which include one girl sneaking into his bed and another freaking out over sending him a text message. In fact it wouldn't be too much of a stretch to declare To Love-Ru one big pile of UST.
Winona and Wallace had a falling out in the past. Wallace is very much still interested in continuing the relationship, even going so far as turning down the Champion position to be a Gym Leader as to spend more time with her. Winona, on the other hand, despite the many hints that she does still love him, has insecurity issues about having a stronger boyfriend. The last we see of the two ends with Winona musing about why their relationship failed the first time.
Sapphire and Ruby aren't much better. Which becomes interesting when you think about who their mentors are. (Hint, look up.)
Hayate the Combat Butler. It's probably the second place for the story's existence. Between Nagi and Hinagiku you could probably drown standing up, and then there's four other girls after Hayate. And that's before you look at Wataru.
Sasameki Koto, There is truckloads of this between Ushio and Sumika from, to the point that it's become somewhat famous for it, which is why the image for the main page features the two. No other series will have you screaming at the characters to "Just get together, already" as much as this series.
Akira and Fumi from Sweet Blue Flowers enter such a phase in the manga, after Fumi confesses to a hapless Akira. It ends in them becoming a couple.
After the Time Skip in Bunny Drop, Rin and Kouki are in this stage. In the end, they don't get together, and Rin ultimately ends up with Daikichi instead.
Spice and Wolf revolves around Holo and Lawrence growing closer and closer over the course of a complicated game of banter and flirtation, while also being kept apart by Lawrence's mortality and other issues. The tension seems like it's resolving itself in incremental steps, however.
Soul constantly uses Maka's lack of sex appeal as the reason for everything from why they don't get along earlier on in the manga to why no one has requested her as a partner in the later chapters. The chapter of Lust, however, would suggest he's lying. Maka also complains that he doesn't refer to her as being like an angel, despite Ox referring to Kim the same way. Doesn't quite work out when you consider the fact that Ox and Kim are boyfriend and girlfriend, not partners. Soul does eventually give in and call her an angel during their fight with Gopher, although he might just be being sarcastic.
Alucard and Integra. It's especially apparent in the manga, where she acts like a Tsundere towards him and he tells her that her resolve and will for battle "excite" him.
Also, Pip and Seras, at least in the beginning.
It gets so bad between Haru and Elie in Rave Master that Lucia, the main villain who spends less than an hour's time total with them over the course of the entire series, is able to instantly spot it and claim they'll be old and grey by the time they get around to holding hands.
Fairy Tail has this developing between Erza and Jellal, mostly due to Jellal's getting arrested or suffering from a massive Guilt Complex. Even having a moment where they end up Literally Falling in Love not getting them together because Jellal stops in the middle of a Kissing Discretion Shot, having decided he doesn't deserve her, and attempts to sink their ship by claiming that he's actually gotten a fiancee over the Time Skip. Erza is aware of the lie, and the two have since been shown looking at each other while the other's back is turned.
The anime plays up the UST between Takashi and Saeko, by implying they may have had sex during episode 9. There's a kissing discretion shot, then it fades to black. The next morning, Saeko appears to be either adjusting her skirt, or her underwear, as she exits the temple behind Takashi. And during the OVA, he hallucinates about having sex with her (again).
Maiden Rose begins right after the Official Couple have just resolved their sexual tension, and then immediately skips six months ahead where UST reappears in full force, especially after Klaus swears to never touch Taki again, thinking that's what Taki wants. It leads to things like 40-panel-long hugs.
This began to emerge between xxxHOLiC protagonist Kimihiro Watanuki and his employer Yuuko Ichihara in the last few volumes leading up to Yuuko's death and disappearance, and stayed for the remainder of the series, at least on Watanuki's end. Aside from the big aforementioned complication, there's the issue that Yuuko tends to keep her feelings distant because the nature of what she sells means it isn't wise for her to allow herself to become too emotionally invested in others. Then there's the fact she also has played something of a motherly-mentor role to Watanuki and is quite a few years older than him.
Though Watanuki later also ceases to age when he succeeds her, so at least that fact in particular would stop mattering so much.
An especially bad case in Yu-Gi-Oh! - in the manga, there was a good deal of this between Anzu and Yami Yugi, with a love tester implying they were more compatible than Anzu and Yugi and him saving her from danger several times. She later said that Yugi is Yugi, and is fine just how he is. However, this triangle mostly disappeared when Yami Yugi begins to become more of a separate identity, with Yugi referring to him having his own feelings and identity. Anzu shows concern when Yami Yugi gets hurt and worries about the effect regaining his memories will have, but her main source of conflict is that she assumed that the real Yugi was a fusion of both counterparts. Yugi never confesses his obvious crush, Yami has little page time solely with Anzu, and Anzu herself bottles her attempt to tell Yami her feelings before the Ceremonial Duel starts.
Also happens with Mai and Joey, and is made worse in the anime when she returns for a filler arc but drives off without confronting him, having turned against Joey specifically prior to this moment.
In Tokyo Ghoul, relationships where the tension is resolved seem to be as rare as unicorn tears.
Kaneki has a whole Unwanted Harem that he seems incapable of reaching resolution with, most notably Touka and Tsukiyama. Both end up having a discussion about whether or not Kaneki is better off without them in his life, while admitting they understand how the other feels about not having Kaneki in their lives. For his part, Kaneki awkwardly goes through cycles of keeping the people important to him at a distance and otherwise avoiding admitting how much he actually cares about them. Finally, Finally subverted with Touka. In chapter 122 of Re, Touka point-blank asks if he's a virgin, leading to a long conversation and eventually ends with them consummating their relationship. Few chapters later, they're married and have a child on the way.
The complicated mess that is Akira, Amon, and Takizawa. She initially seems to dislike them both, with Amon awkwardly trying to gain her approval while Takizawa is her old school rival that complains loudly to his Shipper on Deck mother. By the time the original series comes to a conclusion, Amon has rejected Akira's advances in a moment of guilt/panic, Takizawa has suffered a Belated Love Epiphany, and Akira only admits her true feelings during an Anguished Declaration of Love. The sequel continues this trend, with a tangled mess of resentment and affection leading them all to alternately try to kill or save each other.
Urie and Mutsuki begin to slip into this, primarily from the former's side. Once the two begin to become close, Urie seems to cycle through internal screaming of what he wants to say to Mutsuki but is unable to voice. This leads him to mentally ramble about making sandwiches, how nice Mutsuki's various coats are, how Mutsuki should take a vacation, how he wants to throw Mutsuki a party, and occasionally even blurting out random things. Neither one of them outwardly acts like the other is anything but a comrade, leading to awkward moments between them.