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Solid Snake and Otacon are probably the most blatant who haven't being confirmed as Canon. They've talked extensively about the meaning of love, and make several remarks about how the other taught them how to love. Add to this lots of snarky banter, the natural chemistry between the two as an Agents Dating scenario, and Otacon's famous "I know Snake better than anyone else" line (a recurring line through the series, which is used as a sexual innuendo every other time it is said). Even the voice actors pick up on it.
David Hayter: [Otacon] is just Snake's gay sidekick. In a platonic way.
David Hayter, Snake's voice actor, confirmed that the relationship between Snake and Otacon was supposed to be "romantic", and confessed that they'd played much of their dialogue as love scenes, particularly the 'Bad' Ending of the remake of the first game. The "romantic" nature of their relationship is also evident in the second stinger at the end of MGS4, when Snake decides to live the rest of his (short) life in peace and Otacon doesn't hesitate to go with him. This is possibly the last conversation between Snake and Otacon that the audience hears, and Snake's last word is Otacon's name.
In Metal Gear Solid Mobile, Snake gets out of a Mind Screw when Otacon asks him to remember what it was like when they first met. Admittedly it was played somewhat for laughs because of what actually did happen when they met (from a sufficiently warped mind it could probably qualify as a Meet CuteRescue Romance, come to think of it), but the Does This Remind You of Anything? is still strong.
In MGS4, when Otacon and Naomi started acting lovesick towards each other, Snake looked damned annoyed and really rather jealous, with a hefty side order of heartbroken. (Or Snake was annoyed because of the pure awkwardity of them trying to flirt with each other.)
In Metal Gear Solid 2, Otacon monologues about how he found a 'happy family' and 'learned that [he] could love'. Since his love interest in the previous game was hardly family, it's natural to assume he's talking about Snake, who he seems to be living with.
In Metal Gear Online, Otacon will only sing the victory hymn if Snake is whistling with him.
Quoth Otacon to Snake in Metal Gear Solid 2: "You and your overactive libido."
In Super Smash Bros. Brawl, during the codec call easter eggs, Otacon acts very irritated and jealous during the Samus call ("Yeah, well, Samus is deadly"), and in most of their conversations there's this flirty undertone, especially in the ROB call ("You sure know your geeky tech stuff, Otacon." "Heh heh, well, y'know...").
In Metal Gear Solid 4, calling Otacon while hiding in a dumpster causes Snake to tease Otacon about how gross it is. They laugh together, and Otacon then says, in a flirty tone, that Snake needs to clean himself off before he's allowed to come back. Snake responds, in an equally flirty tone, "I'll see what I can do." (Keep in mind this is a Call Back to the conversation between Rose and Raiden if Raiden gets pissed on in MGS 2.)
In Metal Gear Solid, there's a weird moment where Snake takes Otacon's shoulder and asks him if he's feeling okay, checking for symptoms of FOX-DIE. Otacon accuses Snake of "getting friendly all of a sudden". Snake immediately jumps back a couple of metres and begins to act really coyly - "N-No, I'm just glad you're okay.". In The Twin Snakes, Snake does some much more invasive groping and it's shot through Otacon's eyes, and Snake looks really into it.
Big Boss and Revolver Ocelot give Snake and Otacon a run for their money in the "barely even subtext" category. A Japanese commentary track confirms that Ocelot is in love with BB.
Metal Gear Solid 3 plays out exactly like Ocelot has a crush on Naked Snake. He spends almost all of their encounters desperate to impress Snake, following his advice and improving his technique, with their battle having all the usual MGS homoeroticism ("I've never felt a tension like this before."). He gets turned on by torture for the first time because it was Snake getting it, and after Snake escapes he discovers that Ocelot had stolen his food, to eat the same things Snake eats. EVA hassles Snake repeatedly through the game about how infatuated Ocelot is with him; he remains oblivious to Ocelot's crush, which results in EVA laughing at him. Ocelot disgustedly denies suggested attraction to EVA, yet fails to do so when the same is suggested about Snake. For his part Snake is surprisingly warm towards Ocelot, treating him like a Worthy Opponent and then a close confidant, trusting him enough to tell him his real name.
Gene from Metal Gear Solid: Portable Ops remarks on how Big Boss "caught Ocelot's eye", prompting Big Boss to ask confusedly what Ocelot has to do with anything.
The end of Metal Gear Solid 4 reveals that everything Ocelot had done after Big Boss's death, all the manipulations and quadruple crossing and having his personality buried under a facsimile of Liquid was all for Big Boss. His last words were even "You're pretty good..."
Revolver Ocelot often tosses double entendres in the direction of Solid Snake in MGS ("There's nothing like sliding a long silver bullet into a well-greased chamber."), with Snake flirting back during the torture room scene. He kisses Snake (on the cheek, though) in MGS 4, moans 'Snake...' beforehand, and when Snake gets kissed his Psyche restores. Yeah, Snake's. For that matter, look at the placement of the joystick icon on the screen during that moment. It helps that, as noted above, Ocelot had a canon crush on Snake's identical clone "father", Big Boss.
Volgin sees through the Raikov disguise by grabbing Snake's crotch. If you put on the Raikov mask during the battle with him, Volgin will actually hesitate and stop attacking. EVA notes that a Major having so much authority is unusual, but Volgin basically gave Raikov the power to do whatever he wants. The MGS 4 downloadable plot and character map on the PS Store confirms that Volgin and Raikov are lovers, surprising exactly no-one.
On the subject of Raiden (sort of), his relationship with Snake has to be of the Ocelot/Boss mould. Quinton Flynn does a great job playing Raiden's first encounter with Snake like a mixed-up Fangirl, both mad at Snake for using him like a pawn and jawdroppingly impressed by the fact that it was Solid Snake.
Vamp was sleeping with Scott Dolph, the Commandant of the Marine Corps, circa MGS 2.
Pretty much every single line spoken between Big Boss and Python is Foe Yay-tastic, down to Big Boss recalling their 'training sessions' and Python yelling "Feels good to me, how about you!" before returning fire during the boss battle. It's ridiculous.
Solid Snake and Gray Fox used to be partners, before the latter defected to Big Boss and Snake had to kill him man-to-man. After being rebuilt as the Cyborg Ninja, Fox wants nothing more than to die at Snake's hands, their fight peppered with lines like "Yes, hurt me more! More!", and Fox having screaming orgasms every time Snake hits him, before he performs a Heroic Sacrifice to save Snake.
Try taking a photograph of the anonymous manchest on the door of the open locker near the Engine Room in MGS2, show it to Otacon, and see what happens! Or, if that's not your thing, once you get into the third room of the Tanker hold, show Otacon a full film of photographs of Scott Dolph.
Otacon: Snake, if you like him so much, I'll print this out and make a panel out of it. Put it over your bed or something.
Also, you'll hear Snake say "good" if you manage to take clear enough shots.
EVA seems to have a sweet little crush on The Boss in MGS 3. She talks obsessively about how she's jealous of the very pure love between Snake and The Boss, since she herself only understands sexual love. And moans The Boss's name in her sleep. (She also moans for "Snake" and "Fido", though.)
Metal Gear Solid: Peace Walker has the rather aptly-named Strangelove ranting about The Boss, referring to her as "the woman I loved". She'll also outright state that "naked men are not my cup of tea" if you call her while wearing Swim Trunks.
Cecile is telling Big Boss about her private baths from Strangelove, and when he seems bothered by the idea of Strangelove giving another woman a bath, she responds with a very sensual insinuation that she likes woman-on-woman as much as a heterosexual relationship.
Big Boss and Kaz in Peace Walker seem to exist mainly as Hideo Kojima's attempt to outgay his previous effort of Snake and Otacon, in one single game:
Paz mentions in her audio diary that she saw Big Boss and Kaz fighting, in the showers completely naked, after Big Boss found out that Kaz was sleeping with one of his comrade's girlfriend. She goes into graphic description about the "sweat flying off their muscular bodies", and realises at the end that there's no way she can get between their closeness. The whole thing reads like a slash fic.
Attempting to go on a mission with no clothes on will make Kaz threaten to take off his own clothes "if that's what you want". And then he'll actually do it.
Pictured above, the mission "Date with Kaz". Your objective is to flirt with Kaz and call him to your love box.
In both versions of the game, Kaz taunts Big Boss about parachuting into the jungle 'completely naked', pretending not to understand what Big Boss really meant (he was unarmed). In the Japanese version, he follows this up with trying to persuade Big Boss to do naked skydiving with him sometime. Big Boss isn't too enthusiastic, though.
The Japanese promo "Kazradio" podcast contains little, mostly improvised skits performed by the voice actors for Big Boss and Kaz. In one of them, they visit an onsen, and Kaz slaps Big Boss on the ass. Twice.
There's also this exchange:
Big Boss: Kaz, I want you to go behind me... there.
Ground Zeroes piles subtext about Kaz and Big Boss. Paz calls Kaz's relationship with Big Boss "infatuation", and one of the Japanese-exclusive "Peace and Kazuira Blues" tapes details the "Gay Shower Fight" between Big Boss and Kaz. Words cannot do it justice, you have to listen to it yourself.
In Peace Walker, some of the missions involve looking through the doors of houses to find people inside. One of the 'incorrect' houses is surrounded by the sound of a shower. If you make Big Boss look through, he makes an aroused 'Oooh' sound, which is rudely responded to by a male "Who's there?".
In Metal Gear Rising: Revengeance, Raiden can cut off the clothes of (male) civilians. Doing so will have your support team berating you for "non-consensual activities". Raiden will feebly defend himself by saying it was impulse on his part.