Can't agree with most other reviewers. Firstly, it's not a horror movie. When it was released Attenbrough and cast denied strongly that it was a horror movie at all, presumably to stop it being classed with the kind of movies judged by their kill count and splatter factor. They intended it as a moody ambiguous piece, entirely in keeping with yet superior to a large strand of psychological horror fiction, written and cinematic, produced in the 70's.
Secondly, that said, the character study of Corky Withers is therefore clearly not merely a maguffin to justify some spooky murders, but is in fact the unfolding of the consequences of his personality and choices. Anthony Hopkins puts in a sterling performance, in several voices, to make this happen. Sorry if all that sounds a little pompous and highbrow -- I don't mean it to be.
As to the ambiguity of what's going on -- well let's just say everybody wants to believe in magic. I do believe that was the point.
Anyway, great performances also from Ann-Margret and Burgess Meredith ('What's the first rule of being an agent? Never forget an actor killed Lincoln.'), and a haunting score from Jerry Goldsmith -- one of his better ones. So no, not an action movie, not a killfest, not an episode of The Outer Limits. It is as advertised at the time, a terrifying love story. Take it for what it is and enjoy. I for one am so glad to have found it in DVD.