Tenshi's line asking Otonashi "Why are you still sitting" after he reaches out to her is rather heartwarming given how lonely she seems. This effect is threatened given that until she had asked him that, most viewers would believe she was extremely angry given her general lack of emotion, and that she had started to walk out of the room. Hell, their entire light-romance-ish subplot is extremely heartwarming in light of the tearjerkers that sandwich it.
In episode 3, Iwasawa finally manages to sing 'My Song', coming to terms with her life and finally managing to pass on.
Yui and Hinata talking about how they would meet and marry even if she was paralyzed.
Somewhat more depressing than usual, but when Otonashi uses the last of his energy to sign a organ donor card, which makes all the other surving passengers of the train follow his lead.
Otonashi hugging Naoi at the end of episode 6.
Otonashi: Your life was real too!
It was heartwarming when Otonashi recalls his death and wonders what became of his donated organs and Kanade reassures him that the person receiving them would thank him for the rest of their lives. But it becomes a true crowning moment in hindsight when you realise Kanade wasn't just guessing.
Otonashi's memories of his sister in episode 9.
Episode 10, overall, where Yui gets to live out all of her dreams, including wrestling, winning a game of soccer, playing baseball and finally getting married after being disabled in life.
Hinata explaining how he'd marry Yui at the end of episode 10.
And subsequently the imagined scenes resulting from Hinata's explanation after which Yui disappears.
In episode 12, the source of love that that triggered the doomsday in the afterlife was Yuri all along.
Yuri: I came all this way to protect everyone.
Also in episode 12, the end credits show everybody, even the ones who ascended. It's a nice touch.
Yuri hugging Kanade in Episode 13.
Yuzuru confessing his love for Kanade.
Episode 13 overall.
Yuri's graduation diploma, on which everyone wrote their heartfelt thanks to her.
The Single for Last Song has an incredibly heartwarming moment involving Iwasawa. It includes a six page manga where a young aspiring musician's guitar is destroyed by his alcoholic Father. The boy then finds a CDR labeled Last Song at his feet, he is moved to tears and encouraged by both the song itself and Iwasawa's spirit to work harder at achieving his dream, Iwasawa then High Five's Yui and goes to join the rest of Girls Dead Monster.