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 got resolved before her second death.
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.
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...
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.
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.
Pulp Fiction never resolves the obvious sexual tension between Vincent and Mia.
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."
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.