The fate of the Icarus 1 crew. When Pinbacker sabotaged the Icarus 1 mission, it's implied that they sat together and resigned themselves to their fate, as suggested by the position of their corpses.
This becomes Fridge Horror due to another tearjerker moment that comes later on. After Pinbacker kills Corizon after discovering a new sapling in the remains of the oxygen garden, her dead body is posed holding the new sapling, picked from the ground and basically killed along with her. Basically meaning that Pinbacker may have hunted down and killed all of the crew and then positioned them in the forward observatory of the Icarus I. And seeing how well he was able to dispatch some of the Icarus II crew and set Icarus II's computer to fail in an attempt to stop the mission, it's safe to say he may have done the same thing to the crew of the Icarus I.
Trey succumbing to depression after realizing that his miscalculations have jeopardized the Icarus 2 mission.
The spacewalks of Kaneda and Capa- Kaneda, making a Heroic Sacrifice, turning to face the full glory of a Sun which has been slowly dying his entire life, with Searle whispering, begging, to know what he sees. And Capa struggling so hard to make it to the airlock, stumbling but not failing, to then fly across the surface of the Sun- which he's been having nightmares about- to sacrifice himself for the human race.
The soft farewell Cassie gives to Searle after he chooses to stay behind on the broken Icarus 1 and sacrifice himself to save his crewmates.
Cassie: Searle? We're leaving now. We're gonna complete the mission. We're all thinking of you Searle. Searle? We're gonna go now. We love you.
The crew realizes they will have to kill Trey to survive long enough to drop the payload and reignite the sun-and to do this, they will have to kill Trey, who has become suicidal after needing to repair the damage his miscalculations cause the death of Kaneda. Mace requires a unanimous vote, and finally Cassie results in the most heartbreaking way possible.
Cassie: Make it easy for him.
She's already been through Break the Cutie with Searle and Kaneda’s deaths; now she's been shattered.
Capa's heartfelt last message to his sister, and then when Mace missed the chance to send his last message to Earth, because Capa took long and they flew out of the communications zone earlier than thought. Finally, at the last shot of the movie, we hear Capa's message and quote from earlier again, this time played over a (frozen) Sydney where (supposedly) his sister is. It is as TearJerker as it is Heartwarming, because by then he died, but he saved mankind doing so.
Capa: So if you wake up one morning, and it's a particularly beautiful day, you'll know we made it. Okay, I'm signing out.
Capa's Freak Out when it looks like all life on Earth might die because he tripped over a doorframe in an extraordinarily unwieldy spacesuit. And in general, the physical exertion he has to go through at the end when he has to manually detonate the bomb. And he does all that, having already seen all other crew members die, and knowing the fate of the entirety of humanity is now solely upon his shoulders. All of this doubles as Awesome too, of course.
