Barrow Wights!

I was reading Mist on the Barrow Downs, very late at night by candle light for extra effect.

They are probably the closest thing to a ghost in Tolkien's world. I don't think that he gave any special references about spirits of people lingering around in Arda after they died.
Another thing that creeps me out is the part in the Silmarillion where Luthien and Beren guise themselves in the manner of a giant bat and a were wolf (at least I think it was a were wolf).