Shinji and Kaworu. The blushing, the showering together, the hand-holding, the sleepover, and the declaration of love, all in one episode.
And during the bathing scene, Kaworu places his hand on Shinji's, and rather than hesitate or pull back (as he did in a previous episode, when Misato attempted to touch him), Shinji allows Kaworu's hand to linger on his own. And shortly afterwards Kaworu tells Shinji that he loves him. At the end of the bathing scene, Shinji tells Kaworu that they need to go to bed, to which Kaworu is confused and asks, "Together?" Shinji is quick to decline Kaworu's offer, but he does spend the night at Kaworu's apartment, sleeping on the floor beside Kaworu's bed. Shinji finds it quite easy to talk to Kaworu about his conflicted feelings and Kaworu is shown smiling at Shinji in a fond manner, causing Shinji to blush, and Kaworu tells him "I think I was born just to meet you, Shinji Ikari." Later, Shinji is devastated by his killing Kaworu, and remarks that Kaworu was the only person in his life to tell him that he was loved.
Look where Shinji's staring when he blushes in the shower.
In the movie Death and Rebirth, Kaworu is brought up as a prominent link between the TV series and End of Evangelion. The death scene at the end echos the first scene of End of Evangelion, showing the sheer impact Kaworu's death had on Shinji.
And finally, in EOE, Shinji meets Giant-Naked Rei and has a screaming fit of insanity (to be fair, so did many fans) but a second later, she transforms into Giant Naked Kaworu and asks, "Is this better?" Shinji smiles for the first time since meeting Kaworu. Yep.
During Instrumentality, after Shinji parts from "Reililth", Kaworu appears to him as the representative of the word "love" in Shinji's heart, and is the final proof he needs to reject instrumentality entirety.
In the manga, meanwhile, the Ho Yay is much more sexualized but one-sided, with Kaworu as the aggressor. Shinji outright tells "Evil Manga Kaworu" he doesn't even like him, and rebuffs anything resembling an advance he makes. That still doesn't stop him from kissing a feverish, hyperventilating Shinji in bed—covering it up as mouth-to-mouth resuscitation—then rather aggressively interrogating him on the nature of love. Throughout their scenes together, Shinji is unnerved by Kaworu's "weird" behavior, but acts as a classic tsundere archetype. Only later after killing Kaworu at his request does Shinji admit he was attracted to Kaworu in a conversation with Misato.
Shinji was Tsundere and didn't want to fall in love with him, but did. That's the entire point of their interaction. Sadamoto admitted he was the only of the children who had romantic interaction with Shinji. Asuka and Rei were meant to be platonic from Shinji's side.
In the Campus Apocalypse manga, Kaworu says that he's only helping NERV for Shinji's sake and that otherwise he'd be out there enjoying life until all reality fell apart without him as a Cosmic Keystone.Because Shinji was nice to him, true, but...
Campus Apocalypse Kaworu falls in love with Shinji because they met as children and Shinji patted Kaworu on the head. Kaworu sacrifices himself for Shinji in the end.
After Kaworu reveals to Shinji that he is the final angle he expects Shinji to reject him... only for Shinji to say that he doesn't care. Kaworu turns his head away and bursts into tears of joy.
The Shinji/Kaworu Ho Yay is pretty much confirmed by some of the official artwork available through Gainax's Eva merchandise site.
He gets called Shinji's Orihime in the Evangelion Orchestra Event. It's not only official, but it's the official True Love.
In Rebuild 1.0, Kaworu awakens shirtless on the moon to promptly say "I'm looking forward to knowing you, Shinji Ikari." As lampshaded with many lulz by the fansubbing group, the Japanese word used can mean "to know in the biblical sense."
And in Rebuild 2.0, after knocking out Eva-01 and putting Third Impact on ice, a very annoyed-looking Kaworu says, "This time, only you will find happiness". The creators even jokingly (or maybe not) suggested that Kaworu was annoyed that Shinji had a thing for Rei in this movie.
In the original drafts of Kaworu's appearance, the Ho Yay was meant to be even more blatant. Originally, they were going to go skinny dipping in the ocean together, kiss, and Shinji was actually going to confess his feelings for Kaworu.
The Other Wiki has placed Shinji into the "Fictional bisexuals" category. While this proves little, it does say a lot.
Several games, Kaworu's offered as a romantic choice for Shinji, including the ones he is not a main character (like Secret of Evangelion: Kaworu and Shinji are a Beta Couple to the player's main character and their pairing of choice). In particular the official game, Neon Genesis Evangelion 2, has the official stats for Kaworu's and Shinji's affection as high starter in romantic and low in friendship. While the user can hack and change the parameters, the guide published the official ones, and clarifies they are meant to be perceived as an item (Unfortunate Implications of how this isn't gay because Kaworu's not human, aside), they with the other couples (Misato/Kaji) share a love confession that is related to an event of a good end rather than a generic-love confession recorded for light hearted scenarios that work for everyone.
In the 4koma gag comic strip (not confused with the anime adaptation), Puchi Eva or Petit Eva, Kaworu's blatantly in love with Shinji (he desires to be his wife in his profile and calls Gendo his father in law). There are a number of teases in several strips, including one with Kaworu moving in with his family (the angels) to live with the Ikaris. Yui's supportive of their relationship and teases Shinji about it. For a online Valentine's Day Special campaign in a mobile phone, Shinji and Kaworu were draw sharing the Red String of Fate tied to their pinky, both bashful with a multiple heart patterned background.
In one of the previews for 3.0 has Misato say that Shinji wakes up next to a mysterious boy however this has been disproven as the plot for 3.0 rendered the preview irrelevant. The implication was that the boy was Kaworu, though.
In 3.0 Kaworu and Shinji both play the piano under a heart shaped tree, with Shinji learning how to play the piano instantly with some help from Kaworu. Later on he blushes when Kaworu tells Shinji he can just call him by his first name.
Rebuild's theme songs Beautiful World and Sakura Nagashi are both very much to do with Kaworu and Shinji's relationship.
Beautiful World is rather blatantly about Shinji from Kaworu's perspective, as supported by the male pronoun "boku", and distinctly similar speech patterns. And as for the content... hoo, boy. Who else would profess so selflessly that their only wish is to sleep by Shinji's side? Who sleeps with him in both the original and the films? The singer doesn't care where it is, as "anywhere would do", and in 3.0, Kaworu and Shinji watch the stars together - lying on the cold hard ground. Yet again, the singer's single-minded fixation on Shinji is typical of Kaworu ("I don't need newspapers; they don't have anything important in them/but how are you doing?/if you're alright, then that's good") and also that selfless curiosity and general love of humanity cannot be attributed to anyone other than him - who else would call the world "beautiful"?
Sakura Nagashi is a song about coping with grief, and mourning for a lover deceased. Guess who dies in that film... If the song is read in that light, then the lyrics are very revealing of Shinji's feelings towards Kaworu. ("...You were so beautiful. What would you think of me, living without you?") ("I can't believe we'll never meet again/I haven't told you anything yet.")
Far less blatant is the open admiration Bridge Bunny Maya has towards her superior Ritsuko, though unfortunately for her Ritsuko is far too busy getting banged by Gendo.
In End of Evangelion, compared to Shinji's Kaworu, the figure who Maya sees is Ritsuko who types "I need you" on Maya’s laptop with her hands over Maya’s, and then tenderly embraces her, with her knee planted in Maya's groin. Before she's turned into LCL Maya joyfully returns Ritsuko's hug and cries "Sempai! Sempai! Sempai! Sempai!" with a look of ecstasy on her face as tears flow from her eyes.
Ritsuko and Maya get a Crowning Moment Of Awesome in episode 13, when they defeat the Eleventh Angel by reprogramming a computer. This being Maya, Ritsuko gets excessively fangirled for her contribution.
Let's not forget the onsen bath scene with Misato and Asuka. Through suggestive dialogue and giggling it's hinted that Misato was feeling up her mutually naked charge in some rather provocative ways, under the blanket of being "innocent girlie fun."
Some will also say the relationship between Gendou and Kouzou is loaded with subtext/vibes. Amusing as the idea may be, it's not canon, though you can really imagine what you want with Eva...
And there's a scene in Rebuild 2.0, Kaji asks Shinji if he wants to go on a date with him. Shinji reminds him that he's a boy and in response Kaji says "No problem. Gender shouldn't get in the way of love," places his hand on Shinji's, gets close to his face, and tries (or pretends to) to kiss him and Shinji blushes, letting out an almighty squeal.
Kaji: How about it? Wanna go out for tea? Shinji: You know, I'm a boy.
There's a deleted/alternate scene on the 2.22 DVD where Kaji is introduced in a tram car, which ends with him suddenly saying "I love you" to Shinji before ducking out. So if that had been the final version, Kaworu wouldn't have been the first person to say that to him.
There's also some Les Yay/Foe Yay played with in regards to Asuka and Rei in the official art. Their interactions in "The Day Tokyo-3 Stood Still" actually bordered on a bizarre case of Belligerent Sexual Tension, especially since they made temporary peace with each other in the end. They grow to be on better terms in Rebuild of Evangelion, though.
In Rebuild of Evangelion, Asuka later volunteers to pilot Unit 03 so that Rei can bring Shinji and his father closer together. She does this for Rei, who in most incarnations she doesn't care for at all.
They're on better terms in Angelic Days as well, once even holding hands.
In Neon Genesis Evangelion Gakuen Datenroku, there's a very Les Yay scene between Asuka (playing the Virgin Mary) and Rei (playing Gabriel) during the Nativity Play. Quite frankly, it's impossible to miss. Either that or Asuka and Rei were sneakily insinuating that Jesus is Mary and Gabriel's lovechild.
After Rei reveals her true origins she expects Asuka to hate her, only for Asuka to scream at her that she doesn't care about what Rei is after all they've been through together. Remember that this is Asuka we're talking about, who hated Rei at the beginning.
Hikari and Asuka? Hikari is pretty much Asuka's only friend. And after the battle with Arael, Asuka seeks out Hikari and stays with her for an unspecified time. During a late evening they share a bed and a tearful Asuka breaks down and reveals her inner insecurities to Hikari who comforts her, a testament to their friendship.
The second film of the Rebuild series has a scene where Hikari approaches Asuka and shyly asks if she can sit with her at lunch. She's even blushing when asking it.
And pretty amusingly, when Misato finds Asuka trying to cook, and naturally correctly assumes that she's trying to do something nice for Shinji, for a change, Asuka flusters and tries to insist that it's for a girl. Alas, neither of them seem to think of the implications.
Ikari Shinji Raising Project does this with Asuka/Rei on illustrations and in Shinji's dreams and even in real-life as they become more friendly toward each other late in the series, Maya/Ritsuko, Rei/Misato because Rei obsesses about boobs and can't help touching them, and also Ritsuko/Yui and the terrifying Rei/Yui because Yui has the largest breasts of the whole cast. Also, there is much Shinji/Kaworu to be had and Asuka once jokes about Touji and Shinji having an intimate relationship. And of the more No Yay variety, Gendo simply loves his son Shinji so dearly he wants to bear-hug him from behind or take a bath with him. Look hard and you can probably see some Mana/Asuka too.