Christopher Lee, upon getting the role, read the book, loved it, and underlined entire sections of the book that he insisted must be kept in the film. Without him, there would be no "I know you!" speech in the film.
Molly Grue's seeing the unicorn for the first time. Also falls under Tear Jerker.
Molly: No. Can it truly be? Where have you been? Where have you been? Damn you! Where have you been?! Unicorn: I am here now. Molly: [laughs bitterly] And where were you twenty years ago? Ten years ago? 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! [weeps] Schmendrick: Can you really see her? Do you know what she is? Molly: If you had been waiting to see a unicorn as long as I have... Schmendrick: She's the last unicorn in the world. Molly: It would be the last unicorn that came to Molly Grue. [stands up and hugs the unicorn] It's all right. I forgive you.
In a way, this highlights the difference between our heroes and villains in the story. Molly is willing to let the past be the past and move on, while Haggard desperately holds on to that past for his happiness.
The scene where the bedraggled bandits follow the illusions of Robin Hood and his Merry Men into the woods. Despite the poor conditions they live in, they have not turned completely jaded and are still willing to believe in something more idealistic.
"She will remember your heart when men are fairy tales and books are written by rabbits. Of all unicorns, she is the only one who knows what regret is... and love."
When the heroes manage to free the Unicorns, and suddenly they are joyously stampeding from out of the sea as a virtually extinct species is restored to the world with full vigor.
"I remember you. I remember."
The Unicorn and Schmendrick's last conversation:
Unicorn: You are a true wizard now, as you always wished. Does it make you happy?
Schmendrick: Well, men don't always know when they're happy. But I... I think so. And you?
Unicorn: I am a little afraid to go home. I have been mortal, and some part of me is mortal yet. I am no longer like the others, for no unicorn was ever born who could regret, but now I do. I regret.
Schmendrick: I am sorry. I have done you evil and I cannot undo it.
Unicorn: No. Unicorns are in the world again. No sorrow will live in me as long as that joy... save one. And I thank you for that part, too.
According to Beagle, when he called Christopher Lee to wish him a happy 90th birthday, one of the subjects that came up was the live-action remake.
Christopher Lee: ...if, by the time you come to make your live-action version of your movie, I have passed on, do not let it concern you. I have risen from the dead several times. I know how itís done.