The traditional unicorn is a horse-like creature with a horn protruding from its head, and it has the tail of a lion, a billy-goat's beard, and cloven hooves.
Medieval unicorns are the ones we are most familiar with. They have been romanticized and sadly overused. The most interesting thing I find about unicorns is that they are not native to Europe as would be believed. The first accounts of unicorns are from travelers' accounts while in India, though the Indian unicorn was probably more of rhinoceros type creature than the pristine horse-creature we think of today.
The unicorn originally had many different descriptions, but the most common image is that of the white horse with flowing mane and tale and the single spiral horn sprouting from its forehead. unicorns can be both fierce and gentle. Its horn can pierce anything, though it has to be careful of ramming it into a tree and getting stuck. The unicorn's horn has magical properties, chief of which was the ability to either detect or nullify poisons. For this reason, the horn was much sought after. unicorns can easily be trapped by using a virgin as bait. The pure maiden sits in the woods and the unicorn will approach and place his head in her lap. It is then easy prey for hunters. Besides humans, the other natural enemy of the unicorn is the lion. (The Writer's Complete Fantasy Reference, p 187)
Unicorns are exceedingly rare. Each one you meet will tell you that it is the last one. Their horns, however, are to be found quite often, and you may use them both for healing and as a magic wand. The rumour that Unicorns still acknowledge virgins is probably false. (The Tough Guide to Fantasyland, p 212)
Unicorns are swift, dwelling in deserts or on the tops of mountains. They have a raucous bray and are enemies of the lion. They are most easily tamed by maidens and their shed horn, powdered or cut into pieces, is a wonderful antidote to many poisons. It also has the power to assist greatly in the cure of a number of diseases. (Wizardology: The Book of the Secrets of Merlin)
The Wizardology Handbook has a lot to say on unicorns.
Spring is an excellent time to search the woods fro magical creatures such as unicorns, which may often be found by magic pools or streams. Girl wizards have a particular advantage in the discovery of unicorns, as these creatures seem to harbour naturally friendly feelings towards them, and are slightly ore distrustful of boys.(p 8)
For the best chance of locating a unicorn [as a wizard familiar], proceed to a source of water in a woodland or other outdoor location. Should you be lucky enough to find a unicorn, it will accompany you in invisible form. (p 18)
The King James version of the Bible has several instances of the unicorn due to a translation from the Hebrew word re'em, which is translated to wild ox in the American Standard version. The translation isn't terribly off base. I don't have a specific book source, but I found this about the Re'em online. It basically says that on the Sixth Day of creation, many monsters were created, one being the re'em. Some scholars argue whether the re'em has the likeness of a unicorn, rhinoceros, or a giant auroch. At any given time, only two exist, one male and one female, and they live on opposite ends of the earth. Before the Great Flood, the re'ems went to Noah's arc so that they might be saved. Because of their size, they could not fit into the arc, but Noah saved them by tying them to the arc.
There are many instances of unicorns in contemporary culture.
In The Lion, the Witch, and the Wardrobe a pair of unicorns save Edmund from the camp of the White Witch, and Peter rode a unicorn into the Battle of Beruna in the film adaptation.
Harry Potter encounters a dead unicorn in The Sorcerer's Stone.
It is a monstrous thing, to slay a unicorn.... 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 defenseless to save yourself, and you will have but a half-life, a cursed life, from the moment the blood touches your lips. (Firenze, The Sorcerer's Stone, p 258)
Fantastic Beasts and Where to Find Them, a peripheral of the Harry Potter series, gives a description similar to that given in The Goblet of Fire when Professor Grubbly-Plank gives them a lesson on unicorns in Care of Magical Creatures.
The unicorn is a beautiful beast found throughout the forests of northern Europe. It is a pure white, horned horse when fully grown, thought he foals are initially golden, and turn silver before achieving maturity. The unicorns horn, blood, and hair all have highly magical properties. It generally avoids human contact, is more likely to allow a witch to approach it than a wizard, and is so fleet of foot that it is very difficult to capture. (Fantastic Beasts and Where to Find Them, p 41)
In the BBC show Merlin, Arthur slays a unicorn in the episode "The Labyrinth of Gedref" and it brings a curse on Camelot. In the video game Elder Scrolls IV: Oblivion, the horn of the unicorn is the object of a daedric quest, and the unicorn itself can also be used as a free mount.
There are several other books that mention or are devoted to unicorns, but alas, I have not read any of them. If you know of any additional unicorn sources, feel free to leave links in the comments!