This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Princess Tutu
Episode 2 has Anteaterina's frustration over Rue being better than her.
Episode 3 has Ebine's backstory and her weeping over her lost husband.
Duck's loss of identity early on in the series, as she grapples over who Tutu is in relation to herself and whether she's just a part in a story or not.
It's hard not to feel really bad for the lamp in episode 5.
In episode 6, when Mytho gets the heartshard of fear and becomes terrified of Princess Tutu, Ahiru's breakdown is very upsetting and really marks a turning point in the series. It's not her fault the shards she returns to him are negative emotions, and seeing her pure intentions cause the boy she's trying to make happy whole gallons of pain, it's hard to blame her for sobbing her eyes out. "I just wanted to make him smile!"
Edel's death in the first season finale. The fact that as she burns to death, her last request is that Mytho and Ahiru dance for her does not make it any happier.
In season 2, Duck grows increasingly isolated from what's going on, has no idea what's happening or why, and feels like she can't do anything. It takes lectures from Mr. Cat, Fakir, and a Sadistic Choice from Drosselmeyer to pull her out of it.
Rue's meeting with the Raven in episode 16. Despite terrifying her with threats of violence should she go against his will and emotionally beating her down by calling her ugly and that no one except he and Mytho could ever really love her, when the Raven mentions wishing to see her wedding day, Rue only gives a genuine smile of gratitude and thanks him. Anyone who has ever been emotionally abused and manipulated will recognize that smile immediately.
Rue's dance with ravenified!Mytho is absolutely heartbreaking. He's literally a monster, she made him that way, and she dances with him and remembers how she fell in love with him only to hurt and transform him against his will. It's beautiful and scary and tragic all at the same time.
The last few episodes of the second season will bring anyone to tears. Namely Rue's backstory, Rue's confession and giving herself up to save Mytho, Mytho choosing Rue over Ahiru, and Ahiru giving Mytho up willingly.
The extras on the US DVDs show Jessica Boone and Luci Christian tearing up, as well.
Episode 25 has Duck being driven into complete despair, wondering if everything is her fault, and, at Drosselmeyer's prodding, walking off to drown herself in the lake.
What makes it worse is a heartbreaking shot of her crying underwater as she sinks.
Duck: I thought I was doing my best for Mytho's sake...but was it for my own sake? Just like Mr. Drosselmeyer said...
And later, she tries to tell Fakir that it is her fault.
Duck: Fakir, the pendant won't come off! ...Oh, this is my fault! Because I'm thinking that deep inside my heart I don't want the story to ever end!
Drosselmeyer doesn't just send Duck into the Lake of Despair with his own power, he forces Fakir to do it. Leaving poor Fakir to yell and scream in protest as he's forced to write out Ducks tragic fate.
Fakir and Ahiru's pas de deux in episode 25. You can cry just hearing the music featured during that scene. It's worse when you realize it's The Last Farewell from Prokofiev's Romeo and Juliet. The last scene between Romeo and Juliet before their deaths.
Duck's goodbye to Uzura in episode 25. The music sells it, as does Uzura crying.
The scene in episode 25 where the final heart shard is restored, especially Fakir's narration as it happens. And the music.
Mytho: I never doubted you would come for me. The feelings you returned to me...The feelings of love, affection, sorrow, loneliness...All of my feelings told me that Tutu was sure to come for me. Fakir: Tutu quietly gazed into the prince's eyes, then took off the pendant. The final heart shard was shaped like a pair of fluttering wings. Wings for the people who had spent a comfortable time inside the story to leave the nest with... Fakir and Tutu: Wings for the prince to return to himself with.
In episode 25 when Tutu becomes a duck forever, Mytho bows to her in awe. This music makes it.
Mytho: You were... That something so small and fragile accomplished this... Thank you, Princess Tutu.