This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Tenchi Muyo!
OVA episode 5: Ryoko reminiscing about watching Tenchi grow up from afar (sorta, her conscience was watchimg him while she was sealed away), especially when she could do nothing to comfort him during the sad moments (like his mother's death: little!Tenchi is seen crying and sobbing for his mom, and an also saddened Ryoko can only watch.]]
Specially, two Washu centered scenes from the OAV. First, when she is petting Tenchi's little cousin Taro, who calls her "mama", and she says "no, little child... I'm not your mama..." and hugs him. Second, when after the baby is taken back home, and Washu explains a part of her backstory to Tenchi and the girls - more specifically, about her husband and her estranged child. Yep, the second one goes into a Crowning Moment of Funny as Washu cheers herself up by showing off her adult form, but right before that...
In episode 10 of the OVA, Tenchi finding his mother's kimono and just staring at it for several minutes while recalling what little he remembers about her.
In Universe, Ryouko is mortally wounded and keeps it a secret from Tenchi (even when hugging him goodbye), flies him into Jurai's defence zone, drops him off at the palace, but cannot go on due to blood loss. She pretends she won't go to rescue Aeka with Tenchi and leaves in her ship. Later she dies of blood loss in the cockpit with an odd smile... I shed manly tears.
The only one to see this is Ryo-Ohki. :(
She got better, somehow.
Tenchi in Tokyo gave a very heartwrenching moment when Yugi remade Sakuya and trapped Tenchi in an illusionary world with her. Sakuya decided to let Tenchi go.
During the "Dark Washu" arc of the Shin Tenchi Muyo manga, the titular character gets Hijacked By Doctor Clay and becomes a villain, forcing Washu into a Sadistic Choice: brainwash the others into forgetting her and face her Evil Counterpart alone, or see them get repeatedly attacked. Washu chooses to wipe the others' memory, despite Tenchi being right there when she makes the decision and begging her not to go through with it.
This leads to another painful moment when Minagi runs into Washu and Ryo-Ohki, who ignore her and she runs off to tell the others, only to find out that they have no idea who Minagi's talking about. She's quite distraught that they forgot about Washu until they start thinking harder.
When Tenchi is almost killed by Kagato in the OAV's with only Tsunami's intervention saving him. When that happens, Ayeka is terrified and screams his name in horror, then a prisoner Ryoko frees herself from the trap she's in and goes into space to see if he's still alive. She then finds his scarf, cries a little, and screams 'I WON'T FORGIVE THIS... YOU MURDERER...!!'. Even if Tenchi did survive, it was one powerful moment.