This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Into the Woods
First there's "The Witch's Lament" when Rapunzel gets crushed by the Giantess:
"Children can only grow/ from something you love/ to something you lose...."
And then there's "No One Is Alone", where the characters realize they're not in a fairy tale anymore:
"Witches can be right. Giants can be good. You decide what's right. You decide what's good. Someone is on your side/ someone else is not/ While we're seeing our side/ maybe we forgot: They are not alone. No one is alone."
In the film, there's the part where Jack learns that his mother is dead. The Baker has to tell this kid that he's alone in the world and then explains that the Steward did it. Jack immediately starts planning to kill the Steward for what he did. What really sells it is how Jack talks. While he acts tough, you can tell he's doing his best to fight off tears. After he chokes out, "What the Steward did was wrong!" you can make out that he really is crying. The fact that Jack is actually played by a kid and not an older actor doesn't help matters at all.
And the finale, especially the Witch's reprise of "Children Will Listen":
"Careful the things you say / Children will listen / Careful the things you do / Children will see, and learn / Children may not obey / But children will listen / Children will look to you / for which way to turn..."
Another song by the Witch: "Stay With Me". She sings said song when she finally catches up to Rapunzel after she learns that she had spoken with one of the princes.
This part will make you want to hug your mom:
Who out there could love you more than I? What's out there that I cannot supply? Stay with me...
"Stay at home. I am home."
When the baker finds Cinderella silently kneeling over the destroyed remains of her mother's grave. The tree that granted all of her wishes was killed, and her dreams crushed.
Rapunzel's entire history. Locked up in a tower, banished to the desert, betrayed by her prince and then crushed underneath the Giantess. It's hard not to shed a little tear for her.
Averted in the 2014 film, where she is last seen riding off with her faithful prince. While still less sad than in the play, it still manages to be sad for a completely different reason.
The ghost of the Baker's Wife's entrance just before the reprise of "Children Will Listen".
Baker: Maybe I just wasn't meant to have children. Baker's Wife: Don't say that, of course you were meant to have children.
"Sometimes people leave you/Halfway through the wood/Do not let it grieve you/No one leaves for good..."
It is kind of sad when Little Red Riding Hood discovers that her grandmother and the rest of her family are dead.
Actually, just about every character death in the second act, excluding the Narrator and the Giantess. Hell, even then they're sad in their own way.
The Witch's first response to Rapunzel wanting to stay with her prince and children.
The Witch: You're all I have left.
To be fair, her actions before her transformation did result in Rapunzel's rejection.
Little Red Riding Hood: A wolf and a person aren't the same thing.
The Witch: Ask a wolf's mother.
When The Baker leaves the rest of the survivors, and then the duet with his father's ghost.
The song is cut from the film, but we still have the Baker alone sobbing over the scarf he gave his wife right before she died.
The last half hour or so is just a non-stop tearjerker.
In the 2014 film, Rapunzel reuniting with her prince.
The film's version of "Cinderella at the Grave." Especially the background music as Cinderella's iconic dress and slippers are formed by magic.
In the film, the Baker's Wife finding out about the curse is heartwrenching, no matter how brief that sob was. The poor woman just got told that because of something she had nothing to do with, something that wasn't her or her husband's fault, her greatest desire will never, ever be a possibility.
In the film when the Witch briefly thinks the Baker and his wife failed to get the right ingredients. In most productions the Witch is pissed, but in the film she sits down and breaks into tears. Meryl Streep said in interviews she felt the Witch's only motivation in the film was to prevent losing her daughter, and it comes across here.
"No More" is especially heartbreaking. The Baker is trying to cope with his wife's tragic death, but he can't handle it. Instead, he tries to run away, just like his father had done and is stopped by his father's ghost. His father voices what it was like for him when he ran away, trying to dodge responsibility and figure out how he was going to survive.