Jim Kirk and Spock from Star Trek: The Original Series. They are now the first "couple" listed in Time Magazine's "Most influential People Who've Never Lived". First Couple.
People have edited together various sound clips from the show for this trope. Type "lovetrek" into a search engine if you wish.
There is also an extremely well known German comedy, which has all of the Enterprise crew being gay and got made into a movie eventually (the series was far better, though that was pretty much on purpose), though here it is not only Kork and Spuck that come really close at times, also Schrotti is in the mix...
The Kirk/Spock pairing is also one of the most famous examples of Slash Fic. This would make sense, because (with the exception of some mostlly-clandestine speculation about Holmes & Watson and Napoleon & Ilya) they started the whole thing.
Even the Klingons could see it. In "Errand of Mercy", Commander Kor seems to figure out PDQ that threatening Spock is one way lean on Kirk. Spock would always remain conscious of this even decades later. In Star Trek V: The Final Frontier, after Kirk has been saved just in the nick of time using a Klingon Bird of Prey Spock has commandeered, an emotional Kirk moves to embrace him, leading to this classic line:
Spock: Please Captain, not in front of the Klingons. (Had they been on the Enterprise, well...)
People might consider the whole thing nothing but wishful thinking by some Yaoi Fangirls. In response to this, a fan created The Ship's Closet, a series that carefully analyzes the relationship between Kirk and Spock based purely on evidence found within the show. If you had any doubt, watching this will completely remove it. Or to say it in her words "they don't write romance like that anymore." note The show is currently on hiatus, but Word of God slates it for return in "two months, tops."
She's also going through the episodes here and pointing out the Ho Yay.
Also, apparently, there are rumours about this circulating even in universe.
And when Kirk is asked about it, he just ponders it and doesn't answer. When Spock is asked about it, he usually just raises his eyebrow or glares and doesn't answer.
Also, Also, McCoy tells Spock he feels sorry for him because Spock will never know love. He's talking about the romantic love, like Kirk had for Rayna. Immediately after that, Spock mind melds (a very intimate act for a Vulcan) with Kirk. To examine the mind of the Vulcan, let's take this to its logical conclusion...
And then there's the novelisation of The Motion Picture (written by Gene Roddenberry himself), where Spock refers to Kirk as his "t'hy'la" - a Vulcan word that can mean "friend", or "brother", or "lover"...
Roddenberry attempted to mitigate the effect of this and gently dissuade K/S fans by adding an in-character footnote from Kirk which reads like a mix of evasion and Have I Mentioned I Am Heterosexual Today?. A line-by-line dissection can be found here.
The point has also been made that if "lover" wasn't an important and relevant part of the definition, Roddenberry wouldn't have put it in the definition. Vulcan is, after all, a constructed language.
Spock and Kirk have a tendency to make eye contact and hold it for a beat or two longer than seems appropriate in the situation. Like in Miri, or Corbomite Manuever
In Kraith he even studies on Vulcan to learn how to use them properly. Go ahead, tell us geezers we were naive.
The Wrath of Khan isn't exactly short on the Ho Yay either, considering that during Spock's death scene Kirk and Spock were Vulcan kissing through the damn glass. Prior to this, it took Scotty, Bones, and a third crewman to keep Kirk from going in there to get Spock out...
In The Search for Spock, Kirk willingly sacrifices the Enterprise - the one thing he cares about more than anything else in the universe - to save Spock. Bear in mind that it's mentioned numerous times during the series that the Enterprise is more important to Kirk than any woman and that, in the episode "Elaan of Troyius", it was stated canonically that Kirk's love for the Enterprise was so great that he was able to overcome a biochemical love "spell" cast on him (one that was supposed to be irreversible!) because he still loved the Enterprise far more than the girl. Also in The Search for Spock, there's Kirk saying that if Spock has an immortal soul, it's his responsibility. When the guy he's talking to looks at him weirdly and questions it, Kirk just replies firmly, "as surely as if were my very own." Oh, and he refers to Spock as 'the nobler part of myself.' ('My better half', anyone?)
And Kirk/Ben Finney. When Kirk describes his relationship to Finney, he pauses as if he's got a secret. Ben Finney holds an eternal grudge against Kirk, yet still names his daughter after Kirk. In fact, Finney's daughter only realizes that he's gone insane by reading his letters detailing his obsession with Kirk. Exactly what the letters contained was left ambiguous. Same for the episode "Shore Leave", with Kirk and Finnegan.
Kirk also ends the episode "Obsession" by hitting on a male ensign.
Also, Kirk and Captain Christopher in "Tomorrow Is Yesterday." And Kirk/Gary Mitchell in the pilot.
The ho yay between Kirk and Captain Christopher is hilariously skewered here.
The Janus Gate trilogy of novels basically establishes them as unshakeable life partners, so much so that even when youthful Lieutenant Sulu meets a decades-older Shell-Shocked Veteran version of Chekov from an alternate timeline, they instantly get along. Additionally, toward the end of the series, the older Chekov is forced to kill his timeline's Sulu, whom he's spent most of his life faithfully serving. Established as someone left cynical and emotionally deadened by years of wartime, it's notable that the older Chekov's ONLY display of emotion is at this point, when we see him cradling Sulu's body and weeping with guilt and anguish.
O'Brien told Bashir he wishes Keiko was "more like a man". If that pairing isn't canon, nothing is.
O'Brien: See, you understand! Now why can't she see that? Why can't she be more like y- uh...
Bashir: More like...?
O'Brien: Err, um, a man, more like a man.
"People either love you or hate you...I mean, I hated you when we first met, and now I ... don't. And that's from the heart! I really...do not hate you anymore."
In Extreme Measures we have a line where Bashir tries to convince O'Brien that he likes him more than his wife, states that he likes him better than his girlfriend Ezri, and starts pouting when O'Brien won't admit that he loves him. It should also be noted that in the final episode there are a bunch of montages showing some character's fondest memories on the station. Every. Single. One of O'Brien's memories feature Julian. Not one contains his wife. Also the episode where O'Brien nearly committed suicide, it was Julian talking him out of it and his wife...being useless.
Special mention must go to the episode in which Garak leaves for an incredibly dangerous mission to find his former mentor, and Bashir sees him off. He asks if he can handle any business while Garak is gone, and Garak proceeds to tell him of a very special Cardassian data rod that Bashir should eat if Garak doesn't return. Bashir responds by giving Garak a going-away gift of exotic space chocolates. As one of the YouTube comments puts it:
"So, one guy tells another to eat his rod. The other guy responds by giving the first guy chocolate. The heterosexuality of this situation, it BURNS."
Of course the whole eat a data rod thing is actually a joke. Maybe.
Oh here, an entire playlist dedicated to every moment these two have ever made eyes at each other.
Or when Garak broke into Bashir's quarters in the middle of the night and stared at him until Bashir finally woke up .
And Garak's first words when Bashir wakes up? "Come, Doctor", in his unmistakable creepy voice.
Special mention must go to Bashir and Garak's first scene together. Between Bashir fiddling with the flower like a nervous schoolboy, and Garak going in for the shoulder rub at the end - it's no wonder the actors reacted with Dull Surprise when this became such a popular slash pairing.
"Dull Surprise"? At a convention the two of them outright stated that their characters were having an offscreen "huge homosexual relationship"!
Regarding the shoulder rub, a Cardassian's neck ridges extend down right next to the shoulders and are erogenous zones. It's the first time they meet and Garak's doing the Cardassian equivalent of grabbing Bashir's ass.
Another episode ("Destiny") establishes that Cardassians regard constant bickering as a signal of sexual interest. What have Garak and Bashir been doing every week for three years? Meeting for lunch to bicker about literature. Slashers drew the only logical conclusion.
"The Wire," in which Bashir helps Garak through a near-suicidal drug addiction, is pretty much a forty-five minute canon Hurt/Comfort Fic. It culminates with Bashir going alone into Cardassian space to meet the former head of the Cardassian secret police in order to save Garak's life.
Regardless of the Subtext, Robinson and Siddig's chemistry led to Garak becoming an Ascended Extra, instead of getting killed off early in the series, as was the original plan.
It should also be noted that Andrew Robinson, the actor who portrayed Garak, has explicitly stated that he chose to portray Garak as a sexually ambiguous character, yet, to his chagrin, the series' writers chose to make Garak explicitly straight by the time the character gained some relevance.
There's also a lot of Foe Yay between Odo and Quark. Particularly in The Ascent and in the final episode.
QUARK: So, now that I'm here, is there something you want to say to me?
ODO: Such as?
QUARK: Such as, 'Goodbye, you certainly were a worthy adversary.' Or maybe something with the words mutual respect in it.
QUARK: No? What do you mean no?
ODO: I mean no. I have nothing I want to say to you.
QUARK: You're telling me that after all these years, after all we've been through, you're not even going to say goodbye to me?
ODO: That's right. Nerys, I'll be on the runabout. Huh.
KIRA: Don't take it hard, Quark.
QUARK: Hard? What are you talking about? That man loves me. Couldn't you see? It was written all over his back.
There was always a sexual subtext when Odo would link with another shape-shifter, so when male shape-shifter Laas showed up in "Chimera," some Ho Yay was unavoidable. Odo and Laas link in private, and later, Odo declines when Laas invited him to link in public. And then you've got Quark saying, "This is no time for a 'Changeling Pride' demonstration on the promenade..."
The linking scene between Odo and Laas in "Chimera" shows the two men staring into each others eyes and merging amidst soft background music. It's hard not to interpret it as a quasi-love scene.
Deep Space Nine hinted at Les Yay in the Mirror Universe episodes. Also in the episode "Rejoined", although that wasn't supposed to be about gender.
Kira trying to get Dax on her side in "Dramatis Personae" come off almost like a seduction. Even executive producer Ira Stephen Behr refers to it as "Kira com[ing] on to Dax."
There's also a hint of Les Yay between Uhura and a couple of the alien girls. In Spock's Brain, for instance, when the Eymorg lands on the ship, and the whole crew (including Uhura) gape at how beautiful she is. In Amok Time, when Uhura sees T'Pring's communication to Spock, she says in an almost lovestruck voice "Oh, she's beautiful! Who is she?"
Picard and Q from Star Trek: The Next Generation. Recurring guest star Q develops a fascination with humanity—Picard in particular—and continuously pops up to test him and enjoy Picard's snarky/witty banter. Unless he's popping up to save Picard's life, or guide him to save the universe. He has no regard for Picard's personal space, and pops into bed with him twice; the second time, Picard has a quite civil chat while lying half-nude in bed next to Q. In one instance, when trying to get Vash (Picard's old girlfriend) to come back to him, Q spends far more time talking about Picard, in affectionate and nostalgic tones no less, than he does about the woman he presumably came back for. Not to mention at least one writer and John de Lancie (Q) himself felt strongly that Q was in love with Picard. At one point, Q muses that he might have done better to appear to Picard as a female (presumably as an excuse of using it to manipulate Picard — but the flirty nature of the statement makes that justification come off as suspect).
An example that demonstrates their relationship, from an Expanded Universe novel. Q has whisked Picard off to see beautiful and impossible things, and they have the following exchange shortly before Picard resorts to reciting Shakespeare to comprehend what he is seeing.
Picard: Explain all this, or do you simply enjoy seeing me confused and uncertain?
Q: There is nothing simple about that joy at all, Jean-Luc.
In the Expanded Universe novel "Q-in-Law" Q demonstrates to an audience of people that gender is a transitory concept to him since he can easily assume a female form, stating confidently "I transcend your paltry notions of gender." Q assumes the form of a beautiful woman, and boasts off hand that she was was able to seduce Picard using this form, though the validity of such a claim is never verified by Picard since the subject is never brought up around him.
Best friends Geordi and Data are another example. The closeness of their friendship has been touted since the beginning, as well as their being "bound together" by the nature of the way in which they were forced to see the world: without artifice of coloration.
The Next Generation episode "Suddenly Human" saw the Enterprise rescue a group of aliens, one of whom turns out to be a human teenager who had been raised in the aliens' culture. He wants to go back to the aliens, but Picard wants him to return to his human family and tries to bond with him to convince him to do so. They play racquetball together (in unitards that show off Picard's excellent-for-his-age body), which makes the boy break down crying as he remembers the attack that killed his human parents. Picard holds him and strokes his hair. The boy feels conflicted and goes over to Picard's bedside (he was staying in Picard's room at that point) and stabs him. This makes Picard realize he belongs with the aliens, and the boy goes, but not before doing the touching-foreheads thing that indicates affection in his culture with Picard. There was so much Ho Yay it was just dizzying.
That interpretation is just this side of squick, unless you're an Ancient Greek.
"The Naked Now" is most famous for Tasha and Data getting it on, but what about Tasha and Troi? Tasha's acting all weird, so Troi takes her hand and says, "Tasha, I feel you're very uncertain, that you're... fighting something." And at the end of the episode, they both get off the turbolift at the same time, after not having been seen for quite a while. Hey, Tasha had to be doing someonesomething after Data left...
Yar dies trying to rescue Troi from a hostile alien...
Data's Foe Yay with Kivas Fajo in "The Most Toys". At one point, Fajo throws acid on Data so that he'll change into the clothes he's laid out for him, and then goes on to say that he wouldn't mind if Data just went around naked.
Some of Lore's interactions with Data came off as rather... suggestive to me. In the "Descent" two-parter especially, where Lore gets Data addicted to his emotions and uses that to manipulate him to his side, taking a rather perverse pleasure in it all the while. Lore actually seems to have a bit of a preoccupation with getting Data to work with him, despite the fact that he could have been rid of the other android a long time ago with as many times as he's incapacitated him.
There is a curious example of this trope in the second season episode "The Outrageous Okona" when Worf catches Okona fraternizing with a female member of the crew. Worf orders Okona out of the lady's quarters, but Okona instead takes a step towards the Klingon, at which point Worf growls and says, "I'd love that, but I have my orders!" The intent, I'm sure, was that Okona was acting aggressively, and Worf, as usual, was itching for a fight, but the direction and editing left the scene strangely ambiguous.
And of course, for Klingons, fighting sometimes leads to other things...
In "The Host" Dr. Crusher starts dating a Trill, not knowing the species are actually symbiotes that move through different host bodies. Eventually her lover has to be transferred to another body which is female, and Crusher breaks up with him/her...though it's specifically because she can't handle being with someone who could move to a different body at any time, not that he is now a she.
Seven and Janeway of Star Trek: Voyager. There was a deleted Season 5 scene where Janeway drops a rank pip, which is followed by Seven taking the pip from Janeway and sticking it back on her. Whilst Janeway is saying: "Have you ever considered trying it yourself? Romance I mean."
In S04E25, Chakotay (speaking to Janeway): I know your bond with Seven is unique, different from everyone else's.
The ending of "The Voyager Conspiracy" has got to be the femslashiest thing in the history of the franchise. In the episode, Seven downloads too much data, gets confused, and starts seeing connections and conspiracies where there are none. She steals the Delta Flyer, but Janeway beams aboard to convince her to return. Seven erects a force field to keep Janeway away.
Janeway: There is no conspiracy. There is no Maquis rebellion. The Federation isn't planning to invade the Delta Quadrant.
Seven: I realize that. Because I finally uncovered your true objective.
Janeway: And what's that?
Seven runs through a bunch of dates and events that she, in her confused state, thinks prove that Janeway brought Voyager to the Delta Quadrant for her. Janeway counters with her own list of events, this time all the moments when she and Seven's relationship grew and evolved.
Janeway: Stardate today. Janeway beams aboard the Delta Flyer. She reminds Seven of the bond that's grown between them. Seven lowers the force field, and she decides to come home. All I'm asking... is that you trust me again.
Seven finally does lower the force field. Janeway steps close and sits beside her, and the two stare at each other as soft, frankly romantic music plays. Even when you've already seen the episode it's hard not to think they're about to kiss.
Also, there's the Borg Queen's Foe Yay with Seven. "You were always my favorite, Seven" (while caressing her cheek).
Some fans also saw Ho Yay in the friendship of Harry Kim and Tom Paris:
It helps that Garret Wang, Harry Kim's actor, reportedly wanted his character to be gay, though the producers refused.
The Chute is practically a romance between Tom and Harry. It includes:
Harry (facing down a mob that wants to beat up Tom}:This man is my friend. Nobody touches him!
From the same episode, Tom and Harry discuss like a married couple where the best place is for a picnic. They're in a prison, but that just makes it more slashy.
Tom and Harry cuddling in bed together as Harry comforts Tom as the clamp is driving Tom mad.
So much so that it's a running gag in SciFiDebris's reviews to poke fun at all the accidental Tom/Harry Ho Yay.
Tom and Chakotay has a big following among fans of Rivalry Ships. It's practically slash cannon that the have the tensions they do because they were lovers in the Maquis days and still have some feelings for each other.
The way they touch each other in the opening scene of "the Fight" makes it almost impossible to watch the rest of the episode with your slash goggles off.
In the fourth season two-part Episode "Year of Hell", Chakotay and Paris are taken captive aboard the Krenim time ship for months. In discussing their situation, Paris somewhat sheepishly admits that he has been spending time with handsome Krenim crewmember Obrist. The look on his face as he says it is peculiar, especially since Chakotay has also been hanging around with the ship's tyrannical commander Annorax, so it is not as if there is anything off about associating with their captors. Why be embarrassed? Obrist, for his part, seems very taken with Paris and ultimately does everything he can to help him. It becomes apparent in the end that Obrist did not need Paris or Chakotay to help him mutiny and disable the time ship, he is able to do it entirely on his own. But his actions seem as much motivated by a desire to help Paris as to finally stop Annorax, and he makes a point to beam Chakotay and Paris to safety before lowering the time ship's defenses exposing it to attack.
In the season 7 episode Q2, Q junior and Icheb seem to have this. Admittedly, Q expresses an explicit sexual interest in a number of female characters (including to Icheb), but then, when he runs away from his old life, he brings Icheb along, and later demonstrates that he's willing to die for him. Given that they've only known each other for a few days, I'd say this definitely qualifies.
Then there's the episode where Tuvok loses his memory and latches on to Neelix like a barnacle. And becomes a pastry chef.
Tuvok: Then how will you know how much I enjoy being with you?
Neelix: You've just told me.
Okay, I'm not usually one to see homosexual innuendo in everything, but in "Revulsion", some of the clean-up hologram's dialogue makes it sound like he's outright in love with the Doctor. He even suggests they run away together!
Pick a male character from Star Trek: Enterprise. Newsflash: he has been slashed with Malcolm Reed. Tucker/Reed is the most popular, with Archer/Reed a distant second and Reed/Hayes in third. Something about our dear British armoury officer makes him eminently slashable. Maybe it's all the time he spends playing with phase cannons.