The theme song, as well as the visuals that go with it.
And it seems like all is dying and would leave the world to mourn In the distance hear the laughter of the last unicorn I'm alive; I'm alive
When the Unicorn decides to seek out others, just before she leaves, all of the animals of the forest gather at the edge and stare at her beseechingly. Remember the hunter's speech.
Molly Grue's speech when she first lays eyes on the unicorn, especially her incredibly gut-wrenching, "Where have you been? ...Where have you been? Damn you, where have you been?!" and "Where were you when I was new? When I was one of those innocent young maidens you always come to? How dare you, how dare you come to me now, when I am this?!" Tammy Grimes' vocal performance absolutely has to be heard to be believed.
Schmendrick at first is annoyed Molly would berate a mystical creature like this, but the Unicorn understands completely. In an unspoken moment, she bows her head and Molly whispers, "That's all right. I forgive you." Then there's Molly's response to Schmendrick asking how she can see the Unicorn. "When you've been waiting to see a unicorn as long as I have..."
When Schmendrick informs Molly that she's the last unicorn, Molly bitterly snarks, "It would be the last unicorn in the world to come to Molly Grue." It gets sadder the older you get, and the more you understand.
When Cully's band chases Robin and Marian and the Merry Men into the woods, even though they know it's only a mirage; there's something about that ragged bunch of bullies and cowards believing so completely in an ideal that couldn't be farther from their reality. Because we can't all be a hero or a unicorn.
Brigand: "Robin! Mr. Hood, sir! Little John! Will! Wait for me!"
The sudden choke when Schmendrick rescues The Unicorn from The Red Bull by turning her into a mortal woman... and being old enough to realize exactly what he had just done.
King Haggard's speech, telling Amalthea just why he took the Unicorns, qualifies as this, laying his motivations bare for Amalthea in a bid to get her to reveal herself. In this one scene Haggard is established as a despicable villain who is also a broken, pathetic, all-too-human man. Who, in their life, can not remember one moment of utter joy and bliss? And who would not do anything to make it happen again?
I like to watch them. They fill me with joy. The first time I felt it, I thought I was going to die. I said to the Red Bull, "I must have them, all of them, all there are! For nothing makes me happy, but their shining and their grace." So the Red Bull caught them. Each time I see the unicorns, my unicorns, it is like that morning in the woods and I am truly young, in spite of myself!
The end, where the heroes win the day and hundreds of unicorns, once thought to be all but extinct outside the last one, appear out of the sea to reestablish their place in the world. The music for the scene is the finishing touch.
The main unicorn having to leave the Prince and once again become a unicorn, and the end line about her being the only unicorn who will ever know regret.
"I remember you. I remember."
Just the very thought that the unicorn would be alone having to endure human emotions is painful in itself.
Lir's death. Molly's reaction is heartbreaking but it's the unicorn's reaction that really digs deep and what forces her to put the Red Bull in his place. She was likely the first unicorn that truly had something worth fighting for.
Schmendrick. According to Beagle he's anywhere from being in his 40s or even his 60s, and he's a complete failure. Mabruk greets him "Schmendrick, my dear boy, how nice to see you", but when he finds out he's going to replace him, his open contempt shows through, calling him "The Runeless Wonder". It's plainly obvious Schmendrick feels deep pain every day of his life.
The unicorn's horrified reaction to becoming human, and mortal.
I can feel this body dying all around me!
Lir's parting words to Schmendrick and Molly. It just shows how much of a lonely life he lived.
"I will miss you. I never had any friends before."
The overall tone of the movie. Everything about the film; be it the music, the dialogue, or the characters, is surrounded by an air of melancholy and nostalgia. The themes the characters discuss also evoke depressing imagery, such as depression, lost love, memory loss, regret, resentment towards the past...You better have tissues to last the whole film.
When the unicorn is caged, with a fake horn to deceive the mortals who can't see what she really is, and the villagers see her. They way they all cry, even the men, and the babies reach out... it's like they're having a religious experience (and maybe they are). They're seeing something purely good, so good that it's actually immortal, and weeping in wonder. Gets me every time.
Especially with the one young woman who says nothing, but her eyes are full of tears. Take a second look at the unicorn's reflection in her eyes. It's hard to say, but either it's just the unicorn's ear, or her true horn. If the latter, she can see both horns. She knows it's a real unicorn.
It must be noted that Rukh gave long explanations for each creature, talking about who they are, where they come from, and so on. All he says when he introduces the unicorn is, "The unicorn!" He doesn't need to say another word.
Don't forget the other animals in Mommy Fortuna's menagerie. How many years must the toothless old lion or the ape with the twisted foot have been kept in those miserable cages, and how long could either of them have survived even after the unicorn freed them?
In the book and film, Schmendrick tells Lir the unicorn will remember him long after humans are extinct and "tales written by rabbits".
In the cave near the end, when it's become apparent that Amalthea will likely have to become a Unicorn again, Molly begins berating Schmendrick for it. At first Schmendrick is stoic, then Molly accuses Schmendrick of not caring so long as he gets what he wants, causing Schmendrick to blow up at her and we realize just how much it hurts him how he can only seem to make things worse whenever he tries to help.
Molly: You don't care, you don't care what happens to her or to the others, just so you become a real magician at last! You don't care!
Schmendrick: Well I wish I didn't! I wish to God that I didn't care about anything but my magic, but I do! ...I do...
Just as sad is Amalthea begging Lir not to let Schmendrick change her back to a unicorn, and Lir refusing because it isn't how the story is supposed to go. They both clearly love each other very much, but they both know that their happy ending isn't going to come.
When Molly meets the unicorn and breaks down.
Of Mommy Fortuna's illusions, the most convincing is the spider web that looks to have the whole starry sky trapped in it. The reason it's so convincing is that the spider believes it herself. When Fortuna is killed and the illusions are dispelled, all the other animals run off, and the only remaining sign of life is "the small, dry sound of a spider weeping."
The dog in the cage dreaming of "a hand scratching the lonely place behind its ears."
Finding out that the unicorn had spoken to both Schmendrick and Molly, but Lir had only seen her, and Schmendrick and Molly wouldn't tell him what the unicorn had said.
The Unicorn's reaction to Lir's death.
And the Unicorn screams. An ugly wail of pain and sorrow and loss that no immortal creature ever gave. And the Unicorn turns. She rears up like a scimitar, and her horn shimmers and burns like a butterfly.
The end, when Schmendrick tells Prince Lir, "She will remember your heart when men are fairy tales in books written by rabbits. Of all unicorns, she is the only one who knows what regret is... and love."
Molly's line at the end: "It can't be ill fortune to have loved a unicorn. Surely, it must be the greatest honor there is, if the hardest won."
The fact that in the last two years both Christopher Lee and Tammy Grimes passed away. It makes their performances much more emotional ("It would be the last unicorn in the world to come for Molly Grue..." ...I like to watch them. They fill me with joy...").