This is one of my favorite Rankin-Bass animated features, up there with MAD MONSTER PARTY and THE HOBBIT. A unicorn (voice of Mia Farrow) becomes friends with a magician named Schmendrick (voice of Alan Arkin). They first meet when she's captured by a witch and displayed along with some other animals and he helps her escape. Then, they encounter a band of outlaws in the woods. It's when a huge fiery bull comes for her that Schemendrick casts a spell and transforms her into a young human female, Amalthea. They eventually come to the castle of old King Haggard (voice of Christopher Lee) and learn that he's captured all the unicorns. They have been driven into the sea. Haggard's son, Prince Lir (Jeff Bridges) falls in love with Amalthea, which complicates matters since he'll have to choose between her and his father.
I've always thought this was a great adaptation of the Peter S. Beagle novel--and yes, I like those songs by AMERICA.