This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Rebuild of Evangelion
Asuka's "death" in 2.0. You know it's coming, but still... and that Goddamn song playing when it's happening just makes it worse.
The whole Goddamn ending! Many viewers will already know the Zeruel Event from the original series, so all the changes can be jarring. First, there was the big, fat Hope Spot that was Mari's Bad Ass intervention and her subsequent Crowning Moment of Awesome when she fought in Beast-Mode. She got back up several times and helped Rei out with the Bomb, even with her EVA seriously damaged and a freaking Hole in her side! And then, it ends up failing anyway and Rei pays the price.
Hell, "Give Me Wings" on its own is a huge Tear Jerker if you're in the right mood.
But of course, the biggest Tear Jerker of all was Shinji's fight with Zeruel. Just like in the original series, just when he seems to have grown some guts, his power runs out. In the series, he starts to whine at this part, begging the EVA to move so no one can blame him for the world's end. What does he do in Rebuild? He demands Rei back, even if it means the end of the world! Then, as the Third Impact is about to begin, he holds her tenderly and thanks her for her efforts to resolve his family issues. It may not have been the most reasonable decision, but it was clearly one of the most touching moments in Rebuild thus far. However as of the next movie, he failed; the Rei he knew and loved is dead and the world hates him for triggering the aforementioned Third Impact.
Gendo and Rei's "dinner" together, in a blink-and-you-miss-it moment. Gendo has a full porterhouse steak with all the trimmings. Rei has nutrition pills.
Shinji waking up after 14 years to find that everyone he knows hates him, he didn't save Rei, and he nearly ended the world while at the same time killing so many people.
In 3.0, Shinji unconsciously awakened Eva-01 to help Asuka before she was killed. His reward? WILLE puts him an Explosive Leash in case he loses control again
The state of Nerv HQ and of the whole world as well, the Scenery Gorn in some of the locations of the previous movie and even the original series themselves and the sheer loneliness and abandonment that they irradiate as well.
Everything involving Shinji and Rei or rather, the new Rei clone from Q. First, the girl he was willing to give his life for is dead after all, and when he thinks he found her, what he does meet is an Empty Shell that doesn't react to his attempts to communicate with her. During this, Shinji is shown to know some pretty personal things about "his" Rei, like what books she liked to read. He concludes that the other clone "isn't Ayanami", showing that he really meant it when he said she was irreplaceable to him, and he really suffers having lost his first love. She's only present for a few seconds, but Rei II's presence hangs darkly over the movie. But by the time he's given up on her, Q!Rei has begun some minimal development and is shocked by his talk of another "her" and she becomes increasingly lost and confused, until Shinji's words throw her in an all-out existential crisis.
Kaworu's death and Shinji's reaction to it. We now know what it takes to totally break Shinji. And there is tons of Fan Art being made of it.
It's especially heartbreaking because at the end of 2.0 Kaworu says that he'll 'definitely make Shinji happy', and spends the entirety of 3.0 pretty much achieving that. It isn't until the end of the movie that he realizes what has to be done and that to save Shinji he has to do the one thing that would hurt him the most.
It's not really focused on but when told to kill Shinji by Ritsuko because they can't let Gendo get a hold of him, Misato can't bring herself to do it. Even though she blames him for Third Impact, she still cares about Shinji.
As awesome as it was, the fight in Central Dogma between Asuka and Shinji in 3.33 becomes one in hindsight. None of the two wanted to fight each other and, due the events that happened and their circunstances, they cannot resolve it by talking or reasoning with the other, thus leading to Fourth Impact.
At the end of 3.0 when Asuka finds Shinji in his entry plug. She first states how he didn't save her, adding more salt to the wounds, pushes him with her feet and begins to insult him about how much of a spoiled brat he is, and complains about his catatonic condition while dragging him with her and making him drop the SDAT that Kaworu fixed for him, meaning he tried to take it with him when he got out of the entry plug even in his severe Heroic BSOD. The worst of all is that she is not doing this out of malice, but because she still cares for him, yet the 14 years of fighting have made her unable to show that without hurting him in the process, leaving the two in the same kind of relationship they had in the original series.
Not to mention that it acts as a dark inversion of the hand-holding motif that the movies have shown. Rather than being shown as an act that provides Shinji hope, it is instead shown as Shinji being forced to confront a world without anyone caring about his soul or mental state, as the loss of his SDAT player symbolizes.
"SakuraNagashi", the ending song of 3.0. The melody is sad enough, but the lyrics make it even worse, especially since they can easily be applied to the movie's events:
I can't believe that I'll never see you again
I haven't told you anything yet
I haven't told you anything yet
It seems to be sung in Shinji's POV and is about Shinji mourning for the loss of Kaworu
Pretty much all of 3.0. The movie is depressing all the way through. It feels horribly lonely and claustrophobic, like some terrifying homage to I Am Legend. Shinji has basically committed near-total omnicide and everyone hates him, as we've already stressed. He is reduced to complete uselessness. This movie is literally Shinji's hell. As Asuka notes, Shinji's introverted nature makes him tend towards egotism - he thinks only of himself. He knows this. He hates himself for it. Shinji also has a breakdown about two thirds into the movie which doubles as Nightmare Fuel and while 1.0 and 2.0 had some comic relief, there is no comic relief in 3.0. At all. Notice how early on Pen-Pen has been dropped from the cast? It's going to take some clever writing or an enormousAss Pull to give this anything other than at most a Bittersweet Ending.
The curse of Eva; it locks the pilots to be perpetual teenagers, which not only means they have a harder chance of ever finding a partner, this also means that they a part of them will never mature since the process of growing up is both physical and psychological.
The Evangelion 3.0 OST "Famously . . ." I'm not even going to explain further - the song speaks for itself.