Whenever Roxas or Xion falls into what is essentially a 30+ day coma. The thought of waking up one day to find that your best friend or loved one has fallen into a coma, unmoving for days on end, and, despite being scared and concerned for them, you are ordered by someone higher up to continue with your daily life as though nothing has happened. Oh, god... *sniff*
Everything about Xion and what happens to her in the end. She goes psycho, finding she's a failed Replica and was a tool, then tries to become the original Sora, dies at Roxas's hand, and then fades while nobody remembers her as if she fell into a plothole.
The last part was definitely the strongest one; not just because of what it represents (complete erasure), but also the way it's presented. At first, we see a heartwarming scene of Roxas, Axel, and Xion on their usual spot, laughing, joking, goofing around happily. Some minutes later, the same scene replays; but this time, Xion slowly fades, her interactions with her friends becoming more and more slim, until she vanishes completely with neither Roxas nor Axel noticing. It's not like Naminé who was just forgotten; Xion died completely and then was forgotten. All memories of her are erased from any who met her.
Also note the scene where Naminé and Xion meet. Naminé tells her that she will be erased from existence and everyone's memories. Naminé's power is over memories, but she tells Xion, "I can't save you."
Roxas's line "Who will I have ice cream with?" may seem like Narm until a Fridge Tear Jerker kicks in — he doesn't know any better, he associates his friendship with Xion with their moments on the clock tower eating ice cream together. He lacks the emotional capacity to fully realize what she means to him or him to her, that line is the only way he knows to express himself to her.
The same thing happens when fighting Riku. A cutscene plays showing Riku's memories of her blurring and disappearing. He even tells Roxas, "It's a struggle just to remember the name now, isn't it?"
The final part of the battle against Xion:
Xion: Stop holding back!
Xion's theme is an incredibly emotional piece of music and it nearly threatens you to cry again because it was played during her last moments.
The scene where Xion is curled up on her bed and says to herself, "I'm not a sham." She sounds so utterly depressed, alone, pitiful and broken. It is heartwrenching.
Roxas's final line about how maybe today they'll hit the beach... both because it harkens back to an early conversation and because you know that he never does.
Oh, it's worse than that. His real final line in that "hitting the beach" scene are "Only seven days to go... and then my summer vacation is over." Knowing how that last bit gets repeated at the end of KHII's Prolonged Prologue, it's very depressing.
That line, it's just like, all he went through, and all he lost, reduced to nothing. And yet at the same time, he went through so much and was so hurt and now he has a few happy, carefree moments before he is basically erased, which is basically all that he's destined to be. It's so sad...
The last screen featuring a shot of Roxas and his friends eating ice cream, while on the bottom screen shows him alone, shedding those memories away (along with his Organization coat) was enough to set off the water works again.
The ending scene with Axel and the WINNER stick.
What makes the ending even more brutal is if you look at everything on a large scale: Since his outrage against the Organization (including Axel), the only thing Roxas can believe in is Xion. Who Roxas attacks. After that, he slowly starts to forget Xion, only remembering she was important to him, and that she wants Roxas to release Kingdom Hearts. This being the last thing to him that matters, he goes on a Roaring Rampageof Revenge to The Castle That Never Was, but gets stopped by Riku, who tries to convince him that he is only Sora's Nobody. After that, Roxas gets strangled to near-death, after which DiZ looks over Roxas's unconscious body, saying that Nobodies have no feelings. Then he spends the rest of his life thinking it was all a dream before getting absorbed by Sora.
That and the fact he loses all his memories of Xion before then as well.
Also from Roxas' diary. The thing that apparently frightened him most was the possibility of losing Axel or Xion; that anything could take away the time they'd spent together. Which is exactly what happened.
While playing through Olympus Coliseum, Phil keeps saying he has great expectations for Roxas, and Roxas keeps thinking that means he isn't doing good enough at the training and games. It's like watching the kid who comes from a dysfunctional family try to interact with normal people and not knowing how.
There's also the way Phil so consistently believes in Roxas — the one who, from the moment he was created until the moment he "died", would always be viewed as Sora's Nobody. That Phil sees him entirely in his own light, tells him he has the makings of a champion in him, and treats his existence as having value is a Heartwarming Moment ...that he's one of the only people to do so (save Axel and Xion, sort of) is absolutely heartbreaking.
Even worse, after Roxas' last mission in the coliseum, Phil never sees him again. And he will never know why.
The last thing Phil says to Roxas?
Phil: Don't be a stranger, kid.
The part where Roxas learns to fly. He's just so amazed and so happy that something so awesome has touched his life, a life that the player knows will end up all but erased, all but forgotten.
What is one of the last things Roxas and Axel do before Roxas leaves? They have an argument. It's clear that Axel is trying to cling to their friendship and make sure Roxas stays safe, but Roxas is so lost, confused, frustrated and fed up with the Organization he doesn't even trust his friend anymore.
Even worse in the voiced HD remix, with Kouki Uchiyama and Keiji Fujiwara at the top of their game. The English version with Jesse McCartney and Quinton Flynn is just as upsetting.
Almost all of the above is getting remade into HD with full voice acting. Now we can relive all the lovely memories while dying of broken hearts.
Oh, and something even better? There was a planned Pinocchio themed world, which, as Tetsuya Nomura himself said, "Would've been the saddest point in the story".
In a somewhat meta example, Kingdom Hearts 358/2 Days was Wayne Allwine's (the late voice actor of Mickey Mouse) final performance.
The credits of Days said: "In loving memory of Wayne Allwine."