As far as I know, there is no example of werewolves being immortal in folk tradition. They are merely people (usually men) who have the ability to transform into wolves. It appears that originally the belief was that some men had this ability and voluntarily transformed themselves. This later changed with the introduction of the belief that they were cursed in some way and were forced to transform on occasion. Either way, they are completely mortal: many - if not most - werewolf legends end with the death of the man, having been wounded in wolf form, only to resume human shape so that everyone is aware of the diabolical circumstance of the recent wolf attacks. Then he dies.

The classic works on this are Ella Odstedt, Varulven i svensk folktradition (Uppsaka 1943) and Dag Strömbäck’s article “Om Varulven” in his “Folklore och filologi” (Uppsala 1970).

edit: In partial response to a thread that is not deleted, I can add this:

Tradition is mutating in the modern world because of modern media. Written texts have both drawn upon and affected oral tradition for thousands of years (consider Gilgamesh or Egyptian sacred texts). This latest chapter in this relationship features films recasting folk tradition in new terms. While belief in werewolves has been fading since modernization, there is still a popular knowledge of the motif. Belief is not essential for folklore, and the way werewolf stories are now perceived is heavily influenced by new introductions thanks to film.

Also, a deleted comment that did provide insight pointed out that vampires are not actually immortals but rather animated dead. While this is true in a sense, the response did not capture the nuance of the European folk mind: from the folk point of view, death represented a transition. One could be fated to die and therefore begin the transition even before modern medicine could diagnose a problem. In the same way, people whose heart had stopped - dead by our modern definition - could engage in all sorts of activities that we think of as restricted to those alive. The walking dead from the point of view of the folk mind were people stuck in the transition, neither dead nor alive, but rather dying. Those who were in this transition could be very powerful - someone fated to die could suddenly acquire insight into the future or the supernatural. And those who hadn't completed the transition into the world of the stone-cold dead - even when their heart stopped - could engage in many activities and were regarded as terribly dangerous.

The werewolf doesn't fit into this realm. He is, simply, a person with remarkable supernatural abilities, and because he was typically anti-social (i.e. a pain in the ass to have in the neighborhood) the story usually ends with his being killed.