Their hug at the climax of the second movie is definitely one, too... even if it means the world is ending is the result.
There's also the beginning of Shinji's whole Eva restart sequence.
Shinji: "I don't care about the world... I don't care about anything. I. Want. Ayanami.GIVE HER BACK!"
Slightly less heartwarming when you realize how much that line makes Shinji Not So Different from his father. Then again, perhaps it's more heartwarming, as it means Shinji and Gendo finally have some common ground to stand on.
Made even better by the fact that earlier in the movie, Asuka sort-of confirmed that Rei reciprocates Shinji's feelings even though she doesn't know it yet.
It's a testament to the strength of the scene that you don't care that Shinji has effectively brought about The End of the World as We Know It, because after everything he's gone through, he finally had a triumph.
Rei: "It's alright, Ikari-kun. If I die, I can be replaced."
Shinji: "No! You're the only you that exists! That's why I'll definitely save you!"
Sadly, in 3.0, we are shown that he won nothing since Rei is dead and lost everything since Third Impact destroyed much of the world and the people he used to know are either dead or hate him.
Speaking of Asuka, she had gone somewhat Out of Character by volunteering to test Unit-03 so that Rei can spend time with Shinji, getting almost killed as a result. And that smile on Asuka's face when Rei thanks her via voicemail. Keep in mind: Rei never thanks anyone except Shinji and Asuka, not even Gendo.
In the series, Rei was just ready to blow up herself because she considers herself to be worthless. This time, she does it so Shinji never has to get into an Evangelion ever again. Yep, he left her to basically mope in a corner, and she's still willing to die for him.
She also thanks Mari for helping her nuke the Angel, before ordering her to get out of dodge. Remembering that thanking someone is something that shook Rei to her very core not long before this is a big deal.
Asuka's confession to Misato that although she doesn't want to depend on others, she actually likes the feeling of being nice for a change.
Gendo, of all people, deciding to Pet the Dog and actually go along with Rei's plan to hold a dinner party for everyone, after seeing Yui's face reflected in Rei's. Sure, he goes back to being a total bastard sometime afterwards, but for a fleeting moment, he was content with doing something good.
The moment when Asuka sees the bandages on Rei's hand and then looks at the ones on her own hand. What was about to degenerate into a fight becomes a Not So Different moment.
There is something just adorable about hearing Rei try to describe her feelings.
Rei: "When I'm with Ikari, I feel warm and content. I want Ikari to feel warm and content too."
In 2.22 the moment when Asuka smiles sincerely after a conversation with Misato.
A blink-and-you'll-miss-it moment from 2.22: During the final battle, in the evacuation bunker, you can see Toji protecting Hikari from the impact of the fight going on above.
If Sakura Nagashi is anything to go by, the series will end on a high note.
"Everybody finds love...in the end"
"We will meet again, Shinji-kun".
In 3.0., Shinji breaking into a smile of joy amidst all the chaos of his awakening upon realizing that Asuka survived, and his delight when he sees her again in person (even if the mood is soured by Asuka punching the glass in front of his cell a few moments later).
Depending how you look at it, the moment when Eva-01 saved Asuka when she screamed for Shinji is in a way too. While its debatable that Shinji actually had anything to do with that, the look on Asuka's face afterwards was quite memorable.
Continuing from above, Shinji volunteering to pilot Eva-01 to help Asuka out in 3.0 in the middle of his confusion.
Asuka calling Shinji by his name, instead of simply calling him Test Subject BM-03 like the rest of WILLE does.
The moment where Kaworu is trying to convince Shinji to pilot Eva-13, Shinji is in the middle of a Heroic BSOD from the truth about the Evangelions and Rei. And then Kaworu removes Shinji's bomb choker off of him and puts it on his own neck, telling him that he'll shoulder the blame instead of Shinji, so he doesn't have to worry. It just shows what kind of person Kaworu is to willingly do this for Shinji.
Kaworu and Shinji bonding in 3.0. Shinji has just been thrust into a strange new world where everyone he knew now hates him while it is highly implied that Kaworu is shunned and feared by the rest of NERV due to being an Angel. Watching the two boys find a friend in each other, enjoying themselves and just being happy in what's probably been the first time in a while really makes you smile.
Shinji: "Kaworu-kun, you seem to know everything!"
Kaworu: (smiling) "That's because I'm always thinking about you."
Crossing with CMOA, when Mari is getting Shinji's plug out of the Unit 13, instead of telling him anything cruel like anyone would expect, she essentialy tells him to redeem himself.
Also, as cruel as the ending of 3.0 is for Shinji, Asuka is shown to finally start forgiving him (granted, she can't show that in a healthy way, but it's the thought that counts, damn it!), and the new Rei is beginning to develop feelings.
If you watch closely in the ending scene, you can note that Asuka was panting and had to catch her breath when she reached Shinji's plug, which means in turn that she ran to check on him.
The fact that Shinji doesn't care about the fact that Rei is a clone of his mother so much as that Rei Q isn't the one he saved. Doubles as a Tear Jerker.
The whole movie is filled with moments that evidence Shinji's love and loyalty to Rei, but they're all invariably of the bittersweet sort, because she's dead or worse, trapped within EVA-01. Apparently, he's been paying attention to what she reads. And keeps bringing her tokens of affections throughout the movie. And meant business when he said she was irreplaceable to him. And complements how she looks in her new suit. Too bad it was the wrong Rei...