Actually, they represent the Virgin Mary, Mother of God, due to their weakness for the lap of virgins* (in the progress turning an indomitable beast with a weird quirk sappy**)... oh, wait, you probably think that Catholics are Satanists.
Of course, the coolest unicorn of them all is Al Mi'raj, the Arabian Killer Rabbit.
>Anon-e-Moose:
Alicorn is the substance of the unicorn's horn, the universal antidote cleansing all polution.
>brazenTyrant:
Yes, including the KJV. It is actually a mistranslation of re'em, which is generally accepted to be the aurox. An inconsistent mistranslation, at that, since they actually do translate it as "wild ox" in other places. Oh, and at one point, they turn the horns of the re'em into the horn_ of the unicorn.
* Admittedly, now that I put it that way... might unicorns represent... paedophiles? Wake up, bronies!
** As opposed to the Persian Unicorn, the Karkadann, whose description obviously represents a rhinoceros, that was so ferocious that it impaled elephants on its horn and then died itself because it could not remove the carcass... and still its horn was made of alicorn and it was pacified by virgins.