The legend of the werewolf is quite old -- there are cave paintings of shamans wearing animal skins, suggesting that the idea of men being able to become animals is as old as humanity. Whenever humans first became aware that there was a difference between men and animals, the idea of blurring that distinction must have followed about five minutes later.
In most werewolf lore, the change from human to beast is voluntary, and the person likes turning into a deadly predator. The legendary King Lycaon of Arcadia (whose name gives us the word Lycanthrope) was cursed by Zeus to become a wolf -- but Lycaon earned the god's displeasure by serving him a banquet of human flesh, so the curse just made his bestial nature apparent to all. (It's possible that the Lycaon legend is a garbled memory of some ancient Greek cult with shaman-priests ritually garbed in wolf skins.)
It was only with Curt Siodmak's screenplay for Lon Chaney's film The Wolf Man that the legend finally crystallized around the notion of an involuntary change -- a curse which turns a rational, humane person into a killer. It's no coincidence that Siodmak was writing during the golden age of Freudian psychology.
A number of students of folklore and the occult have tried to discover the "real" explanation of werewolf legends. The late Avram Davidson suspected rabies was the origin. I am suspicious of all such explanations -- surely every person at times has felt himself becoming a beast. The werewolf legend is an object lesson in what happens when we don't master those feelings.
As a writer, I've found werewolves one of the hardest monsters to rationalize. Vampires can be explained as some kind of infection or parasite (as long as you leave out the turning-into-bats part). Lycanthropy is different. At the very least it requires pretty major and rapid body changes -- the kind of wholesale reconstruction one sees when a caterpillar becomes a butterfly or a tadpole becomes a frog. In the natural world such changes take days or weeks, but the werewolf transforms quickly enough to go out, ravage the countryside, get home and change back before the torch-bearing mob can arrive. It gets worse if the person turns into a really big wolf, because the law of conservation of matter raises its ugly head.
Plus there's the issue of only silver weapons harming a werewolf. It's pretty hard to explain why, for example, a bullet or a spear wouldn't hurt someone in wolf form. They seem to affect wolves pretty well. Even giving werewolves improbably fast healing can't quite compensate for the immense damage even black-powder muskets can do, let alone modern weapons.
Still, the pure thematic power of the man-into-beast story means that werewolves are likely to be around in fiction for as long as humans have to worry about controlling the beast within.