A Song of Ice and Fire has, in order of descending Squee fuel, Sansa/Sandor, Jaime/Brienne, and Dany/Daario. Tease consists mostly of the aforementioned characters talking about, thinking about, and dreaming about each other a lot. There also manages to be hints for Lyanna/Rhaegar, even though both characters were dead long before the start of the story.
Also, some fans interpret the whole "Blue rose growing from a wall of ice" business as Jon/Dany shiptease. For the uninitiated, the blue rose is what Rhaegar gave to Lyanna when they first met (Rhaegar and Lyanna being the most likely candidates for Jon Snow's parent). And the wall of ice thing just speaks for itself.
And the title of the series can be interpreted as lending support to the ship as well, with "ice" representing Jon (being the commander of the people who stand watch on the giant wall of ice) and "fire" Dany (with all of the dragon symbolism and the walking into Drogo's funeral pyre and coming out unscathed).
It has Annabeth/Luke, Annabeth/Percy, and Thalia/Luke. But especially with Thalia/Luke - the readers are teased so badly that it's agonizing. And let's not mention their little kiss in The Demigod Diaries
The Sequel SeriesThe Heroes of Olympus has Annabeth/Percy, Ella/Tyson, Hazel/Frank, Jason/Piper, Leo/Hazel, Jason/Reyna, and Piper/Leo. The first four become canon. Leo/Hazel is sunk as Hazel knows she loved his great-grandfather Sammy not him, (and he's confused anyway). Hera sinks Jason/Reyna before it could begin. Piper/Leo is pretty mild with kisses on the cheek, and a shared friendship at Wilderness school neither of them can remember. Percy and Reyna as well. It's fairly common for praetors to become romantically involved and Percy becomes the new praetor after Jason disappears for eight months.
Temeraire has major ship tease with Laurence/Jane Roland. Despite six books and six years since His Majesty's Dragon, Laurence and Jane hooking up at least once, and even a marriage proposal from Laurence, which Jane turns down, readers, nor Laurence, have definitively seen Jane appear in person since Victory of Eagles. Nevertheless, author Novik continues to tease readers with occasional mentions of Jane's activity and goings-on in relation to Laurence and Temeraire's travels.
This ship in particular may have been upped a notch when Granby confesses to Laurence that he is gay in Crucible of Gold, and Laurence admits he may have already suspected Granby's sexual orientation for a while.
Add the fact that Iskierka states she deliberately wants to have at least one egg fathered by Temeraire, and that Granby and Laurence have been close friends, and with Laurence choosing Granby for Iskierka's egg in Black Powder War, Laurence/Granby shippers have quite the array of ship tease to work with.
On a lesser note, a small portion of the fanbase ships Temeraire/Lung Qin Mei, since Mei and Temeraire had a fling in Throne of Jade. Nevertheless, like Jane Roland, Mei has not appeared in the flesh since Throne of Jade, though Novik has also made a few mentions of the Imperial dragoness.
Another fanbase faction ships Temeraire/Iskierka, especially since Iskierka announced her intentions to have at least one egg by Temeraire at the end of Victory of Eagles. Author Novik also continued with more Temeraire/Iskierka ship tease in Crucible of Gold, when it's implied that Iskierka may have gone through all the trouble with the Incan Empress and Maila to make Temeraire jealous, which she succeeded in accomplishing - as well as Temeraire's agreement to mate with her to try and make an egg. However, it's implied that Temeraire seems to be having more than enough trouble with that.
Yet another small portion of the fanbase ships Laurence/Emily Roland, Jane Roland's daughter - despite neither character showing any affection of a romantic nature towards each other [as of Crucible of Gold]; Laurence's and Emily's age differences (Lawrence is in his 30's, while Emily is still a preteen); the fact that Lawrence slept with, and even proposed to, her mother, and the ship being just a little bit creepy.
However, Laurence/Emily has been effectively sunk with Emily showing clear romantic affection, and even aggressive possessiveness, towards Demane in Crucible of Gold. More ship tease for Emily/Demane has since emerged. Blood of Tyrants also established that Laurence regards Emily almost as his own daughter.
In League of Dragons, Novik manages to end the series without making a concrete decision on the matter. Laurence and Jane rekindle their relationship—and it's the most explicit sex scene in any of the books, much made of how Laurence hasn't had any since he betrayed her back in Empire of Ivory and he's unleashing five years of pent-up desire at once. And yet, when the war is over and Laurence retires to be a country gentleman, rather than living on his own or somewhere on his family's estates with Temeraire with the occasional visit from Excidium and Jane, he goes to live on Tharkay's family land, that having finally been returned to him after his lawsuit, at Tenzing's invitation. OT3 anyone?
There's any number of possible ships being teased in The Dresden Files, primarily among them Harry/Murphy, Murphy/Kincaid, and some Harry/Lara Raith, but there's also some Harry/Molly and Molly/Ramirez. There's also other, less obvious ones like Cujo Hendricks/Miss Gard.
Several ships are progressively sunk across the series: Murphy/Kincaid is dead from sometime before or after Changes, Harry/Murphy is an Anchored Ship from Proven Guilty where they acknowledge their feelings but also their emotional baggage and canon from Skin Game until her death in Battle Ground, Harry/Molly is definitively sunk by the end of Cold Days when she becomes the Winter Lady, which also sinks Molly/Ramirez (something confirmed horribly in a short story when Molly finds out the hard way that a) Mab is sparing on detail, b) the mantle of the Winter Lady will viciously attack any would-be sexual partner/sexual assaulter without making any distinction or warning because a pregnancy would shatter the mantle, putting Ramirez in a wheelchair), and Hendricks/Gard is tacitly confirmed and sunk by Battle Ground.
...And then comes the last book, which not only sinks Trouble/Holly but is also one long Artemis/Holly tease. The two of them act rather intimately (like Artemis watching her sleep and Holly stroking his neck) and the scene of them visiting Opal's clone plays out a bit like parents visiting a dying child. Oh, and just about everything in the last third of the book is this.
Book 10 of The 39 Clues had SEVERAL: Some (but not as many as the shippers would have liked) mentions of Ian and Amy, several Hamilton and Sinead hints, some moments of DAN AND NATALIE (gasp!!!), and one mention of Reagan helping Ted draw some diagrams.
Basically the second half of the third book for Amy/Ian, not to mention a small spot where the haughty Natalie blushes when she thinks Dan's complimented her.
In the sixth book, Irina remembers once sharing a meal with Alistair, providing a surprising amount of shipping fuel.
The Ho Yay between Frodo and Sam is well documented and would take up the entire page if more specific examples were added, suffice to say Sam has stated his love for Frodo many times and kissed him multiple times. A lot fans are troubled over Sam's seemly out of nowhere love for Rosy when the previous thousands of pages were about his devotion to "Master Frodo", the movies dialed it up.
Gimli the dwarf has ship teasing with Galadriel the elf queen of all people, since she gave him locks of her hair when he requested. What's more The History of Middle-earth reveals that Feanor, one of the fairest and mightiest of elves, once requested the same thing from Galadriel but she denied him three times, yet when Gimli asks once she happily gives him three locks of her hair and gives him Affectionate Nickname "Lock Bearer". This has heartwarming significance not only because Galadriel showed love to a dwarf despite the deep seated feud of their races but it shows Galadriel could see the greed and pride in Feanor's heart when he demanded a lock of hair and therefore was more willingly to fulfill the more humble Gimli's request. It's also suggested Gimli went to the Grey Havens in hopes of seeing Galadriel again.
Aragon and Eowyn have some moments in The Lord of the Rings: The Two Towers which becomes Ship Sinking as Arwen marries Aragorn and Eowyn hooks up with Faramir in the end.
Legolas and Gimli get as much traction as Frodo and Sam being literally inseparable Platonic Life-Partners. It's revealed in the epilogue that Legolas and Gimli's bromance was so goddamn strong that Legolas refused to sail to the Grey Havens without taking Gimli with him.
Blyton's Malory Towers - If the shipping is kept at the level of 'firm schoolyard friends', Alicia/Darrell or Mary Lou/Darrell might be this, as the first-mentioned girls in both cases seem drawn to the heroine (by jealous possessiveness and worshipful admiration respectively). Alas, Blyton pairs Darrell off in the first book and nobody BUT NOBODY will ever replace Sally Hope as her BFF. Not in canon, at any rate. Averted by Bill, as she states outright (in the third book) that she wants Darrell as a best friend but knows she can't have her.
This transcription of a reading from the then-as-yet-unpublished Captain Vorpatril's Alliance teases By/Ivan pretty heavily. (The novel itself resolutely declines to live up to the promise of the opening, though.)
Fablehaven, starting around Book 3, really enjoys tugging on Kendra's romantic strings. Her attraction to Gavin is immediate and obvious, but he's kind of evil. In Book 4, she meets Raxtus, whom she immediately turns into her own personal in-universe woobie, and they spend the night curled up and sleeping next to one another...but species is kind of a barrier there, since Raxtus is a dragon, and a ''fairy dragon at that. Book 5 seems to set up the Official Couple as Kendra and Bracken, but they themselves admit that relationship won't go anywhere any time soon, due to yet more interspecies shenanigans.
The Last Dragon Chronicles is kind of interesting on this matter. Although the Official Couple is technically David and Zanna, Book 4 introduces Tam Ferrel, who has a huge number of Ship Tease moments with both Zanna and Lucy. Lucy harbors a fairly obvious one-sided crush on Tam, what with her obsession with him, and her excitement over getting to spend time with him. And Tam, during his initial introduction, is interpreted by many people (including Lucy) as hitting on Zanna. Even when she explains that she's taken, they do go on to form a fairly close bond. Lucy does not let this go unnoticed, either.
Gwilanna with Henry, surprisingly.
The Hunger Games is ripe with it, both for the reader and in-universe. Katniss exploits this trope for all it's worth in the 74th games, pretending to be in love with Peeta in order to win sponsors. In the second book it's taken even further. In the Hunger Games movie, it even teased Cato/Glimmer, and a bit of Cato/Katniss, due to the bits where she notices him constantly staring at her.
Fan-Preferred Couple Jayfeather/Briarlight got a fair amount of tease in the Warrior Cats series. While the fact that she lives with him can be overlooked (he's a medicine cat, she's permanently crippled, so it's akin to her living at a hospital), what can't is how she's the only one who can actually get him to stop working and take care of himself. There's also the scene where she breaks down and confides to him how she hates feeling useless to the Clan and how much she wishes she could make something of herself, and he offers to make her his assistant to cheer her up. They frequently cuddle, clean, and/or sleep together, which is something reserved for siblings and mates. She's also one of about three cats who believes him when he says he didn't murder Flametail, which touches him enough to snap him out of his Heroic BSoD.
To take this even farther, when Briarlight dies in River of Fire Jayfeather basically cries, says that Briarlight’s death was his fault and then becomes significantly less sarcastic the rest of the book.
We also have the Finleap/Twigbranch pairing in the Vison of the Shadows series, for example, when Twigbranch wants to leave Sky Clan, Finleap (Finpaw at the time) says that as long as he is with Twigbranch he will be happy.
In The Shadow of Saganami, David Weber ship teases Ragnhild Pavletic (one of the viewpoint characters of the book) with a random Marine. He then blows away their pinnace, killing them both. What makes it worse is that they had been about to board an enemy ship, which would have been an excellent opportunity to introduce said Marine as a Mauve Shirt.
He may be teasing Eloise Pritchart and Thomas Theisman, to whom Eloise has clung emotionally (and physically) since the death of her lover/de facto husband Javier Giscard at the Battle of Lovat. The hand-holding, mutual trust and affection, and their status as each other's primary confidantes could be laying the groundwork for a future romantic relationship — or Eloise could really be an example of The Mourning After, and they're really just Platonic Life-Partners. Weber has been mum on the matter.
Shadow of Victory seems to tease Michelle Henke and Lester Tourville, after the latter is packed off to the Talbott Quadrant to help her attack Mesa. They're noted to get along like gangbusters and there's an undercurrent of flirtation, but nothing overt so far.
Pride and Prejudice manages to tease the notion of Lizzie/Wickham before she learns the truth about him, at which point it teases Wickham and another minor character before he finally ends up with Lydia. Before that, there is plenty of hinting at a Lydia/Denny ship, but she torpedoes that ship herself when she goes to Brighton and returns married.
One of the more famous ships from Pride and Prejudice is Mary/Mr. Collins. After Lizzie turns him down, everyone thinks that he'll propose to Mary, who states that she is fine with the idea. Instead, he marries Charlotte Lucas instead.
In City of Glass, Sebastian Verlac has some sexual tension with Clary and Isabelle, which goes nowhere.
Almost all the romance in Chronicles Of Magic is hinted at, except in a couple cases. Justified, perhaps, in that the main characters are around twelve years old. Special mention, however, goes to Benjamin Burrow and Skeeter Traps. During their own private POV moments, they each think of the odd feelings that they get for one another. Benjamin seems to come closer to realizing it, while Skeeter (being a tsundere) is in constant denial.
In the epilogue of Pinocchio’s Sister, Stashu and Martha meet again and Stashu says she looks prettier than he remembers.
In the book version of The Book of Life, Sanjay and Jane have a few romantic moments with one another.
The later books of Diane Duane's Rihannsu series have some of this between Jim Kirk and Ael t'Rllaillieu, who do grow extremely close over the course of the series. At one point Kirk worries in his Internal Monologue that Starfleet thinks the two of them are an item. (Given that it's James T. Kirk we're talking about, not a surprise.) After she is crowned Empress of the Romulan Star Empire at the end of The Empty Chair, they share The Big Damn Kiss in private before bidding each other farewell.
The kiss between Nathan and Gabriel in Half Wild made a few fans think they would become a couple. Made even worse by the fact that Nathan takes a moment later in the book to recall what Gabriel's hair felt like.
Doctor Who has spawned literally hundreds of novels over the decades, and occasionally the writers have allowed themselves to be a bit freer with regards to depicting Doctor/companion relationships than what was generally allowed on television. Examples include The Dying Days which ends with the unambiguous suggestion (later confirmed in an audio drama spin-off) that the Eighth Doctor beds companion Bernice Summerfield, a Fifth Doctor story from the short story collection Short Trips and Sidesteps where the (supposedly, if you believe the TV show) asexual Doctor becomes distracted when his sexy companion, Peri, wears a revealing outfit. Most recently, the short story "All The Empty Towers" featuring the Twelfth Doctor and Clara Oswald (featured in the book The Scientific Secrets of Doctor Who) contains several ship-tease moments including a plot-irrelevant sequence in which the Doctor and Clara share a dance.
Words of Radiance (second book of The Stormlight Archive): Despite the Adolin/Shallan ship gaining the most steam as they advance their engagement, the particular section of the book where they trudge through the chasms is one big one for Kaladin/Shallan. They work out more than a few issues while there, bare their respective backstories to one another, all with tons of Belligerent Sexual Tension.
The Unexplored Summon://Blood-Sign has numerous examples of this between Kyousuke and the White Queen, despite the latter being an Eldritch Abomination who's utterly Yandere for the former. A major example of this comes at the end of the first volume, where the White Queen leans in almost close enough to kiss Kyousuke, and confidently declares that she's sure he'll eventually save her. He doesn't deny this, simply remaining silent and walking away. After 10 volumes of fighting and character development, They Do.
Good Behaviour: A relationship between Aroon and Mr Kiely is teased, as he drives her home from the Barraway party, and attempts to comfort her. However Aroon rejects him on account of his lower social status
Gaunt's Ghosts: Ever since Necropolis, Ibram Gaunt and Ana Curth have been dancing the ‘will they, won’t they’ fandango, which over the past decade has gone from a mild attraction to Cannot Spit It Out. Even when they see other people, they inevitably go back to orbiting each other again.
There are a few background shipteases too: Brin Milo/Sanian Sanian is revealed to be Saint Sabbat reincarnated, and Milo leaves the Ghosts to join her retinue Ban Duar/Elodie they get married, and ends when Elodie is killed, Rawne/Banda they also become a couple, but it’s ended by Traitor General and Caffran/Criid they become the ‘official couple’ of the regiment, going as far as to raise some aborted kids together. To say it ends poorly would a monumental understatement.
As of Anarch: as the character’s partners have been shot dead or reduced to flying mince, Duar/Criid has been teased, and Rawne/Oyston might well be on the cards.
There are many, many pairings in The Belgariad, but the only proper Ship Tease of the (first) series belongs to Polgara and Durnik, who spend five books being ship-teased to kingdom come (quite literally) before finally getting married in the final chapters of the final book — oh yeah, and saving the universe with the power of their love along the way. They're an established couple in the sequel quintet and in the Framing Device of the prequel novels.
Redwall: The "Where Are They Now?" Epilogue of Mattimeo says that Orlando the Axe became a "firm friend" of Constance and she helped him raise his daughter Auma, who succeded Constance as Badger Mother when she died. This implies that Orlando and Constance may have been in a romantic relationship at one point, but it's never expanded upon.
In Worm, Taylor initially interprets Brian's kindness towards her as attraction - which Brian is quick to refute when she brings it up. They try dating several chapters later, though, and actually manage to make it work pretty well until... well, the below occurs.
of a reading from the then-as-yet-unpublished Captain Vorpatril's Alliance teases By/Ivan pretty heavily. (The novel itself resolutely declines to live up to the promise of the opening, though.)