Unicorns have typically been regarded as one of the cuter, girlier kinds of mythological creature, and there's some sense to that. After all, unicorns are usually regarded as gentle, with magical healing horns, and a particular fondness for maidens. But I guess it really varies.
While modern conceptions often show a unicorn as simply a horse with a horn, other descriptions of the animal have given it features of other animals. The first known person to have made a report of the creature was the physician and historian Ctesias of Cnidus, who described it as a wild ass. Later writings make comparisons to stags and goats. The heraldic unicorn (like the one in the Scottish coat of arms) has a goat's beard and lion's tail. Pliny the Elder wrote of a unicorn as having the feet of an elephant, which adds some credence to the popular theory that the original unicorn reports were really descriptions of the rhinoceros by people who hadn't actually seen the animal.
The link between unicorns and virgins is well-known, with some legends saying that only a maiden can catch a unicorn, and that you need to be a virgin to ride one. I have to wonder how they figured this out, though, and whether they considered the gray areas. Does oral sex count? What if you're a virgin, but have a ruptured hymen? For that matter, what if your hymen is ruptured by riding a unicorn? Will it throw you off? If I ever write anything with unicorns, I'm thinking I might have it revealed that unicorns are really just easily spooked by all but the most docile people, and the maiden thing was made up by a culture with a virginity fetish.
There are several creatures resembling unicorns in non-European cultures. These include the Persian shadhavar, the Hebrew re'em, and the Chinese qilin. The shadhavar plays music through its horn (which would be a pun in English, but I can't say I know whether it is in Persian) in order to attract prey. The re'em is a strong horned animal mentioned several times in the Bible. It was translated to "unicorn" in the King James version, but more recent scholars think that it might actually refer to an auroch. The qilin is a mixture of several different animals, but was typically said to have antlers, rather than a single horn. The Japanese equivalent, the kirin, is generally depicted with one horn, although its body is more draconian than equine.
Unicorns also show up in a lot of fantasy series that I like, including Oz, Narnia, Xanth, Discworld, Harry Potter, and even Lewis Carroll's Through the Looking-Glass (in which Tenniel drew the animal as a caricature of Benjamin Disraeli).
And, of course, the unicorn is highly merchandised, showing up as toys, jewelry, and all sorts of other memorabilia. And I don't think you have to be a virgin to buy this stuff.
Oh, and if I may go totally off the subject, happy birthday to not_glimmer!