The most memorable moments in anime often come when a character hits their low point. The worst thing that they can possibly imagine just happened to them - their loved one died, they lost their job, their depression got the better of them - whatever it is, they just can't function properly anymore.
Some anime characters who hit rock bottom actually bounce back pretty quickly - Simon is devastated by Kamina's death in Gurren Lagann, but he comes back from it stronger than ever. In other cases, it's a downward slide into oblivion - Taizou Hasegawa is never going to stop being a MADAO, and Sayaka Miki's downfall in Puella Magi Madoka Magica results in her death. Whatever the case, seeing characters at their lowest can be a great way to reveal a new aspect of their personalities - or a great way to make yourself sad.
After Tomoya's wife Nagisa dies during childbirth, he completely loses his motivation to do anything. He starts drinking heavily, stops going to work, and worst of all, he completely neglects to play a role in his newborn daughter Ushio's life. Nagisa's parents - who are also grieving the loss of their daughter - step in to take care of Ushio while Tomoya gets his act together, but it takes him nearly five years. When he finally does try to reinsert himself into his daughter's life, it's too late - by this point, Ushio has developed the same condition that plagued her mother and is about to die herself. It's this particular conflict that makes CLANNAD one of the saddest anime in history.
Sukeroku Dies In A Murder-Suicide In 'Showa Genroku Rakugo Shinjuu'
Sukeroku is a talented rakugo performer who can always draw in a crowd. Despite this, the higher-ups in the rakugo community can't stand him, since he refuses to adhere to their standards of decorum. Instead, he does whatever kind of performances he wants to without regard for tradition, dresses shabbily, and spends most of his time outside of work drinking and carousing with women. He ends up losing his career and running away with Miyokichi, a prostitute who is suffering from her own emotional issues.
The two of them move in together and eventually have a child named Konatsu. Sukeroku tries to revive his career but ends up descending into alcoholism. He fails to provide for his wife and child and eventually ends up dying in a murder-suicide orchestrated by Miyokichi. He never puts his life back together, and his story is one of the most tragic elements of the show.
Shinji Ikari has some pretty good reasons for acting out - his father is forcing him to pilot a giant death machine against his will, and talking to him like he's a particularly disgusting insect the whole time. He's deeply depressed, has few meaningful connections with anyone in his life, and he's terrified of what the future will bring.
One of the actions he ultimately takes to express his inner turmoil is disgusting and disrespectful - but it certainly shows how far down the hole he is. When his fellow Eva pilot Asuka is comatose in the hospital, he masturbates onto her unconscious body. It's hard to get much lower than that.
When Sayaka Miki first becomes a magical girl, she's happy enough - after all, she wished to heal her crush's hand injury, allowing him to return to playing the music he loves. Surely making such a noble sacrifice will make him fall in love with her...right?
This turns out not to be true - her crush is unaware that she had anything to do with it and winds up falling for someone else. Sayaka is devastated, and things get even worse when she grows to understand the dark realities of being a magical girl.
All this leads Sayaka to completely lose her sense of self and transform into a witch - who her friends must destroy as they would any other witch. If you didn't want depressing, you picked the wrong magical girl anime.