The soundtrack, by folk band America, is considered by fans to be exceptionally haunting Awesome Music. The opening theme in particular is prone to giving people chills.
Go on YouTube and search for cover versions of the title song, and watch how many versions come up. That's how memorable the song is.
The sequence where the unicorns rise out from the ocean as a tidal wave.
Christopher Lee gives us an absolutely perfect Motive Rant as King Haggard too. A Haggard says that he thought he would die when he saw his first unicorn.
As noted elsewhere, Lee read the book and loved it so much, he underlined entire sections which he insisted be kept in the film, including the Motive Rant. Without him, it risked being left by the wayside.
One for the animators; after Lir falls to the Red Bull, the Unicorn's whole demeanor goes from one of fright, to looking at the Bull as if to say, "You son of a bitch!" The animators capture it perfectly.
Villain she may have been, but Mommy Fortuna goes out beautifully. Having kept the Harpy Celaeno captive for years, knowing one day she would break free and kill her, that day finally comes thanks to the Unicorn. Mommy Fortuna, looking death in the face, simply screams triumphantly that Celaeno will always know Fortuna won. She kept Celaeno, who never escaped without help.
Both the film and the book
Molly Grue's reaction to Schmendrick celebrating he was able to turn a Unicorn into a mortal woman.
Schmendrick:(capering happily) The magic chose the shape, not I. I am a bearer, I am a dwelling, I am a messenger!
Molly: You are an idiot!
Schmendrick finally taking control of his own magic, to successfully cast the spell to transform Amalthea back into the Unicorn. Even moreso in the book, where it's noted that not even Schmendrick's own master had succeeded at such a spell!
When the Unicorn sees Prince Lir's Heroic Sacrifice and decides to charge the Red Bull instead of running from it. She is the first unicorn who had something worth fighting back for. To say nothing of when the Red Bull turns and goes into the sea, defeated — and then a HORDE of unicorns comes charging up out of the sea, running all around Haggard's castle... which then falls apart and collapses into the sea, with King Haggard falling to his doom shrieking in bitter triumph, "THE LAST! I KNEW YOU WERE THE LAST!"
