In J. R. R. Tolkien's Middle-earth legendarium, werewolves were servants of Morgoth, bred from wolves and inhabited by dreadful spirits (fallen lesser Maiar or fëa of Orcs).
They were thought of by Sauron, who was their master and took the shape of a great wolf himself at least once. The Middle-earth werewolves were not shape-shifters like the werewolves of European mythology — they were always in the form of beasts, or at least partially so. The name werewolf appears to have been chosen because they were in essence sentient (but evil), and thus had a status beyond that of normal wolves.
The first werewolf was Draugluin, and the greatest wolf was Carcharoth, the guardian of Angband, a descendant of Draugluin as all other werewolves were. Huan the Hound of Valinor, while also sentient, was not a werewolf. These creatures all lived in the First Age of Middle-earth and are mentioned in various versions of Tolkien's Silmarillion mythology.
It is probable that the Wargs of the Third Age were descended from the werewolves, as these wolves could speak, suggesting they had fëa. Another possibility is that Sauron attempted to recreate the werewolves after his return to Middle-earth, and that the Wargs were the result.
Werewolves are briefly mentioned by Gandalf the Grey in The Fellowship of the Ring, who tells Frodo Baggins that "not all of Sauron's servants and chattels are wraiths; there are Orcs and Trolls, there are Wargs and werewolves." It would seem then that werewolves (or at least their legend) survived into later ages of Middle-earth.