harry potter - What are the uses of Unicorns?

What different uses does the unicorn have?

Other than the delicious taste of them coming off the grill.

_{At Wit's End #221}

Answer

According to Fantastic Beasts and Where to Find Them, unicorn horn, blood, and tail hairs have magical properties. Firenze explains to Harry the cost of slaying a unicorn: (I don't know if this means they will live half the amount of time they were meant to, or if it means they will exist in a unfulfilled, unrealised form.)

‘That is because it is a monstrous thing, to slay a unicorn,’ said Firenze. ‘Only one who has nothing to lose, and everything to gain, would commit such a crime. The blood of a unicorn will keep you alive, even if you are an inch from death, but at a terrible price. You have slain something pure and defenceless to save yourself and you will have but a half life, a cursed life, from the moment the blood touches your lips.’

Philosopher's Stone - Page 188 - British Hardcover

(Does this mean that the unicorn blood that Voldemort consumed in Philosopher's Stone affected his lifespan in any way? Perhaps it helped Harry to ultimately defeat Voldemort in some unknown way. . . ?)

Unicorn horns are silver and are used in potions (Harry notices them at the apothecary in Diagon Alley during his first visit there with Hagrid.)

As noted, the unicorn tail hair is used as a wandcore by Ollivander. Harry also mentions using unicorn tail hair as an ingredient in Potions lessons. ETA Unicorn blood is an ingredient in Voldemort's initial resurrection potion which allows him to return to the infant form that Wormtail carries around, that we see in the beginning of Goblet of Fire. I didn't mean to say that it was in the resurrection potion used in the graveyard in Little Hangleton. Unicorn blood was used for the initial potion (Goblet of Fire - Page 569, Brit version) along with Nagini's venom. Just wanted to clarify.

Strangely, Hagrid tells Harry:

Harry saw that Hagrid looked very worried.

‘Could a werewolf be killing the unicorns?’ Harry asked.

‘Not fast enough,’ said Hagrid. ‘It’s not easy ter catch a unicorn, they’re powerful magic creatures. I never knew one ter be hurt before.

Philosopher's Stone - Page 183 - British Hardcover

I wonder how Quirrell managed to even catch one unicorn, much less two. Yes, he has Voldemort inside him, but Voldemort is in a very weakened state and cannot perform magic independently yet. I digress.

Professor Grubbly-Plank in Goblet of Fire indicates that unicorns prefer a woman's touch to a man's, although I don't know to what purpose this serves. The unicorn apparently has numerous magical properties:

Professor Grubbly-Plank’s voice carried over to the boys; the girls were all clustered around the unicorn now, stroking it. [SNIP] Harry turned to stare unseeingly at the unicorn, whose many magical properties Professor Grubbly-Plank was now enumerating in a loud voice, so that the boys could hear too.

Goblet of Fire - Page 383 - British Hardcover

Hagrid uses unicorn tail hair to bind up bandages on injured creatures and mentions that unicorn tail hair is very strong (HBP - Page 455 - Brit). He collects stray hairs that he finds in the Forbidden Forest and keeps a bunch of them hanging from the rafter in his hut.