This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Eureka Seven
Episode Six. You may think it's a comedic, light-hearted episode about Eureka's kids playing pranks on Renton, you're half-right. The scene where the kids are crying and they said that they didn't want Renton around because they think he's going to take Eureka (their adoptive mother) away is pretty heartbreaking.
When Ray fails to avenge her husband Charles' death and her ship is falling to pieces around her. Suddenly her eyes snap open and she says, "Where? Where is it?" Her arm has been torn off in the burning wreckage, and she slowly crawls with one arm across the bridge to where her severed arm lies... for the wedding ring that lies on it. And then, just as she's about to reach it, with a sad, hopeful smile on her face, the ship explodes. Not to mention this is all combined with flashbacks of Charles promising they'll have a great future together even after she turns out barren.
Oh, yes. It probably wouldn't have been so bad had there not been a few episodes showing what nice people they are, how they genuinely loved Renton, and were even planning to adopt him.
The worst part of that episode where Ray is going insane after Charles' death is that... she sets the table for her, Charles, and Renton with their 3 mugs.
And the worst part of the whole arc is that none of these tragedies had to happen. Charles and Ray start their vendetta against Gekkostate because Dewey convinces them that Ray's infertility is Eureka's fault. If they had ever learned the truth...
If you've watched this series before, then the episodes where Renton is happy with Charles and Ray. It only makes it that much worse when they're so accepting and loving of Renton, even supporting his decision to go back to the Gekko if that is what he wants and is determined to do.
The only reason why all the crap that Gekkostate put Renton through in the first 12 episodes was remotely tolerable was so that he could be with Eureka. So when Eureka turns him away after desperately trying to tell her his feelings for her, he pretty much loses all hope and decides to leave the ship.
Some of the flashbacks involving the slaughters that Holland and Eureka committed during their time on the SOF are pretty heartwrenching.
Anemone's behavior when she goes out to pilot TheEND for the last time. In a brutal contrast to her normally spastic behavior, she alternates between listless self-hate and wistful regret. Renton, Eureka, and the kids with them are even driven to tears! And to make things worse, she finally admits her love for Dominic, the boy she's treated horribly for most of the series, but concludes that it's far too late.
Anemone: If, after this ends, someone were to tell me 'It's okay to live', I'd buy just one small mirror and practice smiling. I'd practice over and over, to meet you again. Maybe, if someone were to tell me 'It's okay to live without hurting anyone', I'd pull back my hair as it tossed in the wind, and I'd take a giant step. I'd push out my chest and go see him. I want to live... I want to tell him 'Thank you'. I want to live to show him my feelings. I want to live... It would've been better if I hadn't discovered this feeling.
After this, Anemone prepares to unleash her ultimate attack on Renton and Eureka when Dominic falls from above, calling out for her. By the time she notices him, it's too late for her to stop her attack from launching with him in the way. While he narrowly avoids being killed by it, the look of horror on her face is indeed heartwrenching, though it is immediately followed by one of the series's most triumphant CMOHs.
That little girl and her parents on the plane.
Speaking of which, Episode 23. The Beams are on a mission to bring a Vodarac girl, who is living in critical condition and refused service by the hospital, to be brought to her final resting place. Having none of it, Renton desperately tries to save a Vodarac girl from dying by taking her to another hospital across town. However, the girl is harshly discriminated at the hospital he does go to; and when they go back, it's too late.
That same episode, Eureka finally realizes her feelings for Renton. And then Holland breaks the news that Renton jumped ship... Where's my Kleenex box again?
It's more sad once you consider one of the reasons behind Renton leaving the ship was the fact that, as Eureka didn't understand that she "loved" him at the time, he believed that Eureka hated him.
Episode 25. William B. Baxter really deserves a prize for not losing his composure and becoming depressed when his wife catches the Desperation Disease.
One of the biggest tearjerkers in the series didn't come from the anime, but rather its manga adaptation. Despite defeating the Big Bad, Eureka eventually succumbs to her wounds. The final interaction between the two lovers and Renton's reactions makes it brutally difficult not to cry.
While this troper was saddened by her disappearance, the manga also implied that one day Eureka will return (once the Scub is restored), so he has hope.
When TheEND dies. Especially so soon after it's transformation, and the way it just looks down at Dominic and Anemone in happiness as it protects them, as though its happy that the two are finally together.
"Renton... I want to see you."
The heartwarming parts all around 'Pacific State' aren't enough to make one forget how absolutely BROKEN Holland is at that point, still hurting from his injuries, clouded by indecision, and filled with regret from how much of a jerkass he was to Renton. And it all comes to a head when Talho takes the crew down for lifting, and Holland decides its his last one, and it is far from glorious. He pushes himself too far, Talho begging him to stop in tears, and when she gets by his side, we get this:
Holland: (tears flowing, and in a sad, slightly mocking voice) I'm so pathetic Talho. I'm pathetic, aren't I? I'm sorry... the only thing I had any talent for... was lifting.
Talho: But... you still like it, don't you?
Holland: Yeah... I love lifting. And this planet that lets me lift. That's why I can't forgive the existence of beings that want to destroy it. Talho... no matter what happens from now on... I want to protect this planet that I met you on. And you for loving me despite being so pathetic.
Episode 44. Dominic discovers the horrible experiments that Anemone was forced to endure early in her life. Not only that, but the deaths of those three girls and countless others combined with the Lack of Empathy is heartbreaking.
Episode 45. When Maurice threatens Renton with the Rifle because he thinks Renton is stealing Eureka from them.
The climax of episode 49.
Holland: "It was too late for me to realize it. I wasn't able to save my own brother."
Talho: "Yes. Everything was too late. Every single thing we did, we did too late."
Eureka: "I can't keep my promise. I'm sorry Renton. Bye bye..."