See, the thing with immortals is that they always have some kind of curse or weakness that ENDS the immortality. For example, a vampire is immortal...unless you stab that sucker with a wooden stake through the heart. Many other kinds of immortals have such a weakness. Aside from that one, usually obscure, weakness they are impossible to kill. Some movies are centered entirely around figuring out that weakness while avoiding death; many horror movies for example.
On a side note, one of my favorites is seen in, The League of Extraordinary Gentlemen
, a fantasy/action movie.