Tim Drake (Red Robin) and Cassandra Cain (Formerly Batgirl) from DC Comics. Word of God from Damian Scott (a penciler of many Batgirl comics) is that the pair "kind of act like they're in love, but just don't know it". There's this image on that matter as well.
X-Men: Quite a bit between Gambit and Storm, despite the former's romance with Rogue. Tellingly, their friendship has soured a bit since the latter's marriage to Black Panther.
There's also the Cyclops/Jean Grey/Wolverine love triangle, which never was resolved before her second death. (Unless you count Cyclops and Jean getting married as 'resolving it.')
Superman and Lois had a good 55 year run of this in the comics (although, their Earth 2 counterparts tied the knot decades ago, they got together in the movies, and they had even started dating in the comics current continuity about 6 years prior). Superman was either too Super for an earth woman or too alien or he had to stay dedicated to his mission. Post-Crisis, it was more that he wanted Lois to love him as Clark since he considered that to be his True Self.
Superman and Wonder Woman. Supes has always had Lois, but Diana has gone for long stretches without a steady boyfriend (poor Steve Trevor kept getting written in and out of continuity). Elseworlds stories sometimes depict them getting together after Lois and Steve have died, since Clark and Diana may be ageless.
Spider-Man and Ms. Marvel when written by Brian Reed (later picked up by other writers, including Kelly Sue De Connick in an arc of Avenging Spider-Man).
Link and Zelda have this in the Valiant Comicsseries based on the originaltwoZelda games. It's only unresolved because she doesn't want to admit she returns his feelings; if it were up to him, they'd probably be married already. At the end of the Nintendo Power series based on The Legend of Zelda: A Link to the Past, Zelda tells Link that the link between them was so strong while she was in Ganon's clutches, but now Link is so distant and she is alone. She will never forget the time they were together in their dreams...
Weightless, Garrus and Shepard had this bad before she was spaced. And after she returned, they continued to do this for a good couple of chapters before eventually get on with it.
One of many as yet unresolved sub-plots in Discworld monster Slipping Between Worlds concerns the interaction between visiting bemused Roundworlder Philip Holtack and young graduate assassin Jocasta Wiggs. This is a Work In Progress, but Word of God is that there are a few twists in store yet.
Of Love And Bunnies, a Power Rangers fanfic, takes this tack with Tommy and Kim, the original Green/White and Pink Rangers, who were in a relationship until it was terminated by a "Dear John" Letter. The first hundred or so chapters build up the UST that resulted from 5+ years of not seeing each other and it's still going on despite them figuring out that Skull broke them up by accident.
In the NarutoFan FicA Wrinkle in Time, Naruto and Hinata. The only reason they didn't get together in the future is because of the war, since Naruto was Hokage and Chief of the Joint-Shinobi Alliance. Even then, it's explicitly stated that if it hadn't been for Hinata's untimely death, something would've happened between them eventually. Her death almost drove Naruto over the Despair Event Horizon and into committing suicide. One of Naruto's goals after going back in time is to ensure that he and Hinata live long enough to finally have a chance together.
The same happens in Naruto:Asunder. While they are close and live together, they're still Just Friends since Naruto is unsure if he genuinely likes her or if she's a Replacement Goldfish for (the recently deceased) Sakura. Not helped by Naruto's upbringing leaving him unsure of how to proceed. By the time they decide to resolve it Madara's plan kicks off and they end up dying. Everyone Can See It however, what with Shino's father casually calling her "Uzumaki" Hinata and In the sequel (Naruto:Rend), Gaara is quick to comment on how given time they would've been married had shit not hit the fan.
What Hath Joined Together: Lock Flash Sentry, somepony with a major Bodyguard Crush on Princess Twilight Sparkle which may be reciprocated, in an empty train with the object of his affections for twelve hours, and you get two very, very uncomfortable ponies.
The Avengers (1998), between Steed and Mrs. Peel. They flirt throughout the movie, but can't get together because (as in the original series) Mrs. Peel's husband is missing (and presumed dead), so he could show up at any time.
In the first Teenage Mutant Ninja Turtles movie, Raphael develops a crush on April some time after he rescues her from the Foot; he's noticeably bashful when she thanks him for rescuing her and she returns the favor by staying by his side when he's put into a coma to make sure he doesn't get killed. But the tension between them is not brought throughout the rest of the movie or any of the sequels.
Cairo Time. Unresolved sexual tension is the plot of the movie. Seriously, nothing happens but sexual tension. Absolutely nothing. And yet it's lovely. In that Brief Encounter sort of way.
Drinking Buddies explores UST between two old friends who also happen to be in relationships with other people.
In Inception, Arthur asks Ariadne to kiss him so that Fischer's dream projections don't detect them.
Arthur: Quick, give me a kiss.
(Ariadne kisses him, then looks around.)
Ariadne: They're still looking at us.
Arthur: Yeah, it was worth a shot.
There was pretty much no way the projections would have refrained from attacking Arthur. They can sense the dreamer and don't care what he's doing. Arthur just wanted Ariadne to kiss him. The kiss is never brought up again.
If you watch her face, she doesn't really seem to mind being tricked. It's not brought up again since they spend the rest of the film in different dream levels.
Lost in Translation: The entire movie is about Bob and Charlotte's sexual tension and them trying to resolve it despite both of them being married.
Frantic, the 1988 thriller by Roman Polanski. There's loads of unspoken sexual tension between Harrison Ford's character and French smuggler Michelle, but as Ford is desperately searching for his kidnapped wife nothing happens.
The sexual tension between Mia and Vincent in Pulp Fiction causes Vincent quite a bit of alarm, given that he believes her husband threw a man off a second-story building just for giving her a foot massage. He even has a Mirror Monologue to give himself the strength to leave her home without screwing her. Ultimately her overdose kills the mood anyway.
The Audrey Hepburn film The Nun's Story has UST between Sister Luke (Hepburn) and the doctor she works for, Dr. Fortunati (Peter Finch), while she is in the Congo.
Star Trek IV, between Kirk and Dr. Gillian Taylor (Catherine Hicks). "Like they say in your century, I don't even have your telephone number."
There was alot of lesbian sexual tension in the film Black Widow between Alex and Catherine.
James Bond's UST with Moneypenny is one of the staples of the series, though theirs is more lighthearted than most examples.
One of the many things The Searchers is famous for is the completely silent interactions between Ethan and his sister-in-law, which most people interpret as an unspoken form of this trope.
Thor and Sif of Thor. Intentionally done by the writers, since the people who worked on the film wanted to be able to have the option of writing Thor/Sif into the sequels, should they later want to.
Jaimie Alexander: (about Thor and Sif) But there is a reason that we sort of subtly hinted to it in the first film. Just so that there is a door. If we want to go through that door, we can. They like to cover all their bases at Marvel.
During an interview, Chris Hemsworth referenced this when speaking about their relationship in the sequel, as well as what it was throughout the first movie.
Chris Hemsworth: In the comic books there’s obviously an attraction with Thor and Sif, or what have you. And there was little peppering of that, I think, in the first one. Little hints at it. There (in the sequel) may be… might be more indication…
Molly and Nomi of Showgirls. The two constantly cast longing glaces, become inexplicably close friends almost immediately, lounge around in their underwear and intimate that they have masturbated together. This is parodied in the off-Broadway parody "Showgirls: The Musical!", in a song called "Best Friend Song". Lyrics include: "Men don't know how to write female intimacy/unless we are finger-banging or scissoring/So let's hang out in our underwear, let's hang out in our towels/We'll spend all night masturbating because we are best pals!"; and "We're best friends now, we probably should have sex/'Cause that's what best friends do when the writers are men!"
Nell and Theo of The Haunting. In the remake, this is more overt, as Theo becomes explicitly bisexual, whereas in the original, it was only implied.
The music video for Wham!'s Club Tropicana provides a twist on this, when George and Andrew are revealed to be airline pilots, and backing vocalists Dee and Shirlie are flight attendants.
The Yaghan people of South America actually had a word for this trope. It's 'Mamihlapinatapai' and roughly translated, it means, "A look shared by two people with each wishing that the other will initiate something that both desire but which neither one wants to start."
Quite blatant in two of the three routes in Fate/stay night, especially the second. The third route avoids this for Sakura as they resolve it rather early on. However, it does apply in the epilogue between Rin and Shirou, wherein it has apparently been going on for years; Sakura gently teases the two about not being honest with each other about it.
Except in the True Ending for Kara no Shoujo, Toko and Reiji have immense amounts of UST that is picked up on by the rest of the cast, who come to the conclusion that they must be sleeping together.
Pleasure Bon Bon, plenty of it between William/Wilson and Mary, the former of whom is posing as gay to keep a job as a butler for the latter's overprotective father, and the former of whom .....really wants some tube steak in her
Gallons of this between Gil and Agatha in Girl Genius. Almost to the point of parody.
There's also tension between Agatha and Tarvek. It's not for nothing that one of the images for the Girl Genius website's main page has one of Agatha's clanks running off with her diary, shedding love letters to both Gil and Tarvek.
Emily and Ash from Misfile. Twelve books, over 1200 strips, and three kisses, only one of which was actually consensual. Not to mention extremely awkward.
In It's Walky!, to such an extent between Joyce and Walky that when it was finally resolved, it nicely mimicked the effects of a small thermonuclear device. The collateral damages were... significant.
There's a good bit of this in The Space Between, between the protagonist Jack and his childhood friend, Sam. It starts to come out when Jack and C.J. hook up at their house party.
The three protagonists in Platinum Grit are swimming in unresolved sexual tension. Jeremy is too repressed to admit to anyone that he fantasizes about Nils. Kate is too embarrassed to admit to anyone that she's developing a major crush on Jeremy. And Nils is too defensive to admit to herself that she's falling for Jeremy.
Ansem Retort, of all things, has a bit of possibly-unintended tension between Zexion and Namine. Namine was impressed when Zexion sold territory to Mexico for a new name, Zexion knew immediately who had swapped his cyanide pills with Mentos, he detoured from his booty call with Belle to brag to Namine, and Namine has developed a psychic "Zexion-sense" alerting her that he was in trouble (though she didn't feel the need to DO anything about it). They claim to hate each other but spend a lot of time together anyway, and it's been noted that Zexion likes his women "blonde, dumb, and not totally dead inside"— Namine fits two out of three (after Zexion, she's probably the smartest cast member, despite being introduced as a Cloud Cuckoo Lander). It probably won't go anywhere because of her age, but...
Zexion threatens to have sex with everything Namine loves... and Namine retorts that she loves herself. The next time we see them, they've... resolved their tension.
UST in Errant Story persisted for literally years between Jon and Sarine, until there came a deliciously ironic subversion/twist: it finally got, one would say, resolved ... but things became so uncomfortable afterward that Sarine used some mind magic to de-resolve it. And then it was back to more years of UST, which was still there as the story approached its end.
From Homestuck, there's some of this between Dirk and Jake. But while Dirk is definitely seriously about wanting to go ahead with it, Jake has doubts, and isn't sure whether his feelings are actually strong enough. There was also some between Jake and Jane, but when Jane claimed she didn't actually have a thing for him, he admitted he was actually kinda relieved they could just be friends.
Due to the incredibly complex Troll attraction system, it's safest to assume there's a lot of this going around between all of them.
Karkat and Terezi. Their complicated dance of attraction, friendship, romance and enmity defies human comprehension, especially since both of them have had Ship Tease with at least two other people.
Echo Chamber features an entire episode dedicated to UST, in which Dana lets her hair down and Tom voices his approval. He gets flat out rejected, but The Stinger indicates that that rejection may have been a front.
Thalia's Musings has this between Thalia, the Muse of Comedy, and Apollo, Governor of the Muses.
The Autobiography of Jane Eyre: There is strong UST between Jane Eyre and her older boss E.D. Rochester. In episode 11, their hands keep getting really close and they are almost touching. In episode 13, Mr Rochester is visibly smitten with Jane, and grateful to her for her gentle care when she takes broken pieces from his wound and bandages his bleeding arm. Jane probably likes him too already, but her feelings are more mixed because he has a kid, is her boss and is obviously troubled with something serious. It's based on Jane Eyre, so the resolution might be guessed.