The Main Character and Akinari, the Dying Young Man. One of the fanbooks has relationship charts for each social link, and Akinari's depicts his and the MC's relationship with a heart around the bench they sit on.
And don't forget Minato and Ryoji, which is the most popular Ho Yay ship in P3 for Japan.
In the female path of the game, Ryoji reveals that he would like you even if you were a boy.
The New/Full Moon drama CD series spells it out that the main reason Pharos became Ryoji, instead of going to fulfill his duty as Death, was because he wanted to continue spending more time staying by the MC's side.
Speaking of social links, French exchange student Bebe (Temperance) is quite affectionate toward the main character, to the point of waiting outside his classroom in the higher levels of the link. Not to mention that his plot, which revolves around him trying to find a way to convince his uncle that he belongs in Japan, can be read as a metaphor for coming out.
Not to mention him and the protagonist having a "delectable time" when they went to the candy shop after their first Fashion Club meeting together.
The Lets Play plays this for laughs, with the Main Character having a very blatant guy-crush on Bebe.
Kenji Tomochika (the Magician/Classmate Social Link) giving the protagonist a choker at the end of his Social Link because 'he doesn't look fashionable enough'.
Surprisingly, there's some between Shinjiro and the Main Character. The former often expresses his concern for the latter's health, especially after the MC recovers from his cold in September. In one of the Drama CDs, Shinji even makes food for him while the MC's sick.
Talk to Junpei on 4/29 and answer "No, we're going.":
Junpei: Listen to me, man. We shouldn't go tonight. Besides, it would be just you and me there. You know, like, Brokeback Tartarus.
Aigis acts exactly the same as she does in the original even when you play as a female. She is also the only female character who will privately see FeMC off in a tender moment during the ending.
In the her 8th and 9th social rank, Aigis goes through something that looks suspiciously like Gayngst. And confesses to the female character at that!
Aigis's feelings are barely even subtext — I mean, what else could the thing she wants in relation to the protagonist that she can never have because she's neither human nor male possibly be? And the max rank event has heavy sexual overtones as well. She takes the MC to her room, asks her to touch her intimate inner, uh, robotic workings, and then you get the "you spent a long time with Aigis" message with fade to black...
Mitsuru asks the female protagonist to hold her hand while watching a scary movie.
She even asks the FeMC to live with her during her Rank 9 event, after asking her to run away with her during rank 8.
Way back, in the beginning of the game, right after you fight the first Shadow, you'll meet with Yukari again before going to school. If you've act nice to her up until that point, she'll blush as she says your given name for the first time.
When Yukari has to wear a maid outfit for her club's school festival cafe the Fe MC can tell her "I'm looking forward to it!"
That doesn't even begin to cover it. A lot of the links for the FeMCare subtext-riffic. Her Hermit Link, Saori, could easily be read as having a crush on her. A lot of the holdover 'romantic' links have... interesting vibes too, like with FeMC/Fuuka- the Max event has the two of you baking a cake, taking it to Fuuka's room, talking about how you're going to be bonded forever (or in Fuuka's case, wanting the FeMC ALL TO HERSELF), and then you get the fadeout screen with the 'You spent a long time with Fuuka'- the exact same message you get when you max out romantically with a guy. For a game without an explicit lesbian option, they sure do cram in as many non-explicit ones as humanly possible... not that I'm complaining.
Selecting the 3rd option during the last date with Elizabeth leads to some very suggestive dialogue. To top it off you then receive the same "You spent a long time with so and so" message that you get from the male love interests.
On that note, in 'Portable' you can choose to have Elizabeth or Theodore as the attendant in the Velvet Room. The route for the dates stays the same, and since you end up inviting Elizabeth into your room and 'spending a long time with her'...
Persona 3 suggests such a connection between Fuuka Yamagishi and Natsuki Moriyama, in the way that Natsuki gets really stressed out when she thinks her bullying may have hurt Fuuka a little too much. SEES has to keep Natsuki under constant watch because they think she might have some... issues.
Natsuki wasn't afraid here bullying might have hurt Fuuka a little too much. She was afraid her bullying may have KILLED Fuuka. Anyone would react as she did to the thought that a seemingly harmless prank may have accidentally killed someone.
It's still played straight after they become friends.
Mitsuru also has a particular fangirl that hangs around the main classroom and dreams up elaborate fantasies about her.
Said fangirl is also Yandere and Ax-Crazy, to the point of blackmailing over people for pictures of and items related to her.
And then there's one of the 'bonus' videos added for FES. You know... the one where Yukari drags Fuuka into her bedroom and starts pulling her clothes off so they can pose in maid outfits together? Sadly, the video cuts off there...
Akihiko and Shinjiro's relationship in particular seems rather complex.
Aki/Shinji is the most complex relationship, and I swear there's more then enough Ho Yay. All their scenes together, that Akihiko confronts Shinjiro about taking the persona suppressants, and that Akihiko holds Shinjiro during his death. It's far more then just random shipping.
More humorously, in the manga's rendition of the Lovers' full moon battle, Akihiko and Junpei end up in a similar situation as Minato and Yukari, and it ends with Akihiko punching Junpei in the face.
Not to mention that, in his MAX Rank on the lover's path, before he'll do anything, he asks FeMC to call him "Aki" - as in, the nickname only Shinjiro called him.
And poor "Aki" feels quite awkward around girls, and even chatting them up.
Jin and Takaya. They hold hands. They go everywhere together. They scheme to kill all of humanity together. They run a hitsite together. And Takaya's last line of the game is "Jin." Ho Yay? For sure.
Not to mention Jin's bottomless devotion to Takaya is his main motivation for following the plan to bring about the Fall, therefore "fulfill[ing] Takaya's wish". It just makes one wonder what else Takaya could convince Jin to do for him...
Jin holds Takaya's hand twice, to stop him from "being reckless". If that's not enough to go on, when they jump off the bridge, it looks a lot like lovers suicide and the second time, he's practically begging "Don't Go!" when he looks up at Takaya.
This might be a stretch, but Takaya and Jin are always referred to as partners, which doesn't go without a double meaning; Akihiko in particular sounds scathing when he says it, but Jin doesn't care. Hmm...And while they're part of a trio, but they don't seem to care much for Chidori, especially since they kill her.
Also, this is probably just a coincidence, but Takaya and Jin's names are similar to Tatsuya and Jun, a possibly canon Ho Yay pair in Persona 2: Innocent Sin.
Junpei and Ryoji have no shortage of Ho Yay, oddly despite the fact that they're both ladies' men. Only a few weeks after Ryoji first shows up, he and Junpei are practically inseparable, to the point of being out on the town together the night Junpei's girlfriend is kidnapped.
Yukari and Mitsuru have a lot of Les Yay.
For starters, in the Male MC route during the fight in the Love Hotel, the team gets separated, and when you meet Mitsuru and Akihiko or Junpei again, Mitsuru will frantically insist that nothing happened. When you play the Female MC route, you can potentially meet up with Mitsuru and Yukari, and she'll insist the exact same thing.
Something of note about Mitsuru's resolution: From that point on, Mitsuru decides to start calling Yukari by her first name. The only other people worthy of this privilege? Akihiko(a close friend from years back) and the MC...at rank nine, long after the S-link has gone romantic. If that doesn't say something about how Mitsuru views Yukari after her resolution scene, nothing does.
Plus during December when everyone is deciding whether to kill Ryoji or not, Misturu comes into Yukari's room and they discuss things. They come to the same conclusion pretty quickly and they both sit on Yukari's bed ....but nothing ever becomes of it. Lampshaded perfectly in this Let's Play.
Yukari crying into Misturu, and what looks like Mitsuru holding her to her chest during The Answer.
"Well, that's settled, let's go have a bath!"
The New/Full Moon Drama CD series focuses more on their relationship and much of their dialogue can be interpreted as romantic.