It was Xion's death that really got me.
She's first introduced as a character that has the same powers as Roxas, so the Organization uses her to collect hearts at twice the rate Roxas was able to do, and she eventually becomes best friends with Roxas and Axel. Then she loses her Keyblade and gets it back, but by then she's already questioning her existence. She leaves the Organization, which is the beginning of the disintegration of the friendship between her, Roxas and Axel. Soon she meets Riku and Mickey, and she learns about herself being just a failed copy of Sora, the protagonist of the Kingdom Hearts and Chain of Memories who was put to sleep to repair his memories after CoM, but because Roxas is Sora's nobody he naturally is a part of Sora, isn't going through much of the same drama Xion is because she is made up of the remaining memories not used to create Roxas. This means that in order to wake Sora up with all his memories repaired, both Xion and Roxas would have to die.
Eventually, the Organization, including Axel, dismisses Xion from their cause as a traitor, much to Roxas's annoyance that not even his best friend will tell him what's going on. He also leaves the Organization, and meets Xion. At this point, Xion is upset in her failed existence and believes that the Organization created her to absorb Roxas and become a perfect copy of Sora, therefore ensuring the real Sora never wakes up to stop their plans. She attacks Roxas in a final fight before she is ultimately struck down by Roxas. As she is fading away, she explains to Roxas that the Organization was evil and that he absolutely cannot let Xemnas have his way. After a long, saddening speech made by Xion, she fades away, leaving Roxas (and the player) to cry. A lot. Now that half of Sora's memories are returned, everyone that has ever had any sort of interaction with Xion at all forget about her, including Roxas.
The very sad thing about this is that she wasn't even the final boss of the game. She was the penultimate boss of the game. Roxas, even though not being able to remember Xion by name, tries to undo Kingdom Hearts so he can get her back. Riku, the games final boss, taunts Roxas about Xion's disappearance and telling Roxas that trying to undo Kingdom Hearts was a very bad idea. Even though Roxas is the victor in the fight between them, Riku taps into the darkness inside him, turning him into Ansem, the final boss of Kingdom Hearts and Riku's story of Chain of Memories, and instantly knocks Roxas out. Later, a man named Diz talks to Riku about Roxas as the camera pans out.
We see Roxas wake up in the opening for Kingdom Hearts II, blissfully unaware of Xion, the Organization, or anything that had happened during the game. He wakes up to go visit his friends Hayner, Pence, and Olette, saying "today we'll finally hit the beach!", before the camera pans up to the sky, and a song by Hikaru plays, it's slow tempo and piano strikes hitting you in the emotional gut.
It's even worse if you've already played Kingdom Hearts II, because Roxas isn't aware that this memory was just a fake Diz made while trying to keep the Organization out and waiting for Namine to finish fixing Sora, where Roxas will ultimately fade, just like Xion.
What makes this scene even sadder is shortly after fighting Riku. On the bottom screen of the DS, the next two cutscenes after that fight will play a cutscene where Xion, Roxas, and Axel are eating ice cream and enjoying each other. The first cutscene play it normally, and on the second cutscene it plays the scene again, but this time Xion is gradually fading until she is removed completely by the end of the cutscene playing on the top screen. It's an experience I can't describe by just writing about it, you'll have to either play the game or look it up on YouTube to know the feeling.