In SEED Episode 40, during the Heroic Sacrifice of Uzumi Athha, who tells his little girl Cagalli that although she was adopted, he was so glad to have been her father before spiriting her off to freedom, Fiction Junction's Chariot of Dawn acting as a heartbreaking funeral march did not help to stop the tears from pouring down. Damn you Yuuka for your beautiful singing voice!!
Kira's response: "Maybe this was all a mistake." His girlfriend is breaking down in front of him, and he's too emotionally drained to deal with it. Highlights how badly both their lives suck. Made even worse when Kira refuses to see his parents, noting that, "all they'd see is a soldier" and that he'd have to ask "why the hell they made me a Coordinator."
"This is what I do: I pilot a mobile suit, and when I'm not fighting, I help other people build mobile suits. Why? Because I can."
Perhaps one of the biggest reasons for why Flay's death was more tragic than she deserved was not just because she truly regretted her actions and behavior in the series, but because, in the end, she was never able to properly make amends with Kira or Sai, or anyone else, which is what she desperately wanted to do now. And, if that weren't enough, according to Word of God, Flay's spirit never actually appeared to Kira, meaning while we got to hear what Flay wanted to tell Kira, he never did. It's somewhat better, however, knowing that Kira still forgave and loved her regardless of her never being able to make things up to him. He's just that kind of guy.
Nicol's death. Made worse when you realize that the episodes leading up to it foreshadowed it to high heaven.
Followed by Tolle's death. My God, poor Miriallia... *sob*
And the scene that follows that: Kira and Athrun beat each other down in what is probably one of the most brutal Gundam fights ever animated. All while sad music is playing. Here are two best friends, who still care for each other after all these years... and they're trying as hard as they can to kill one another, both out of rage at the loss of their comrades, and out of a feeling of sheer futility in trying to deny that they are enemies now.
There is a short scene in one of the last episodes, showing the inside of a hangar full of damaged Strike Daggers and an Earth Alliance pilot holding another one in his arms, screaming for a medic. We then see the face of the carried pilot who has blank eyes, either an indication of being dead or in coma.
Find the Way, the final ED for the series, is most certainly Tear Jerking Music. Both the song itself and the imagery of the credits screen really tugs at you.
Another small moment is the sinking of Vesalius, with Captain Ades saluting Athrun, Dearka, and Yzak as fire engulfs the bridge.
Early in the show there is the Mutual Kill of EA Admiral Lewis Hallberton and ZAFT Captain Zellman, with each man sacrificing himself for the future of his side. Ramius and Nicol's near simultaneous Say My Name moments ("Admiral Hallberton!" "Captain Zellman!") drive it home.
From that same episode, Yzak shooting down a shuttle full of civilians. On that shuttle was a sweet little girl who had made a piece of origami for Kira. Kira's breakdown in the following episode when he sees the origami and remembers what happened was even worse.