"The Empty House"
by Algernon Blackwood
A young man and his elderly "maiden aunt" (who is interested in "psychical" phenomena) decide to investigate a haunted house together.
It's a spooky short story-- but it's "old-fashioned spooky", which means modern readers may find it a bit tame. I thought it was alright, and now that I see that it goes along with a whole collection of short stories by the same author, I may try a few more.
One More SPOILERy Note:
I did feel that the story ended rather abruptly and was a little flat. When it was written, maybe it would have been more than creepy enough, but reading it today, I thought it could've gone further.
I suspected, after they saw the ghostly woman in the scullery doorway, that the aunt had been somehow possessed with the victim's spirit. Various things from that point on seemed to support my theory-- how quiet she was, how much braver she was than the nephew had expected (stunned/not herself, I thought), how her face momentarily looked like that of a young woman, etc. (Of course, there were also things that made me doubt...) I thought it would eventually be revealed, when they left the house, or right after the ghostly climax, that the aunt hadn't been herself through most of the night and didn't remember anything after the shock at the scullery door.
Later, when they heard/felt the two people running down the stairs and the one being thrown over the railing, I had a new ending in mind. They'd walk downstairs. The man would see his aunt lying on the stone floor and realize that she hadn't really been beside him since they left the upstairs room. He'd instead been accompanied by the victim-ghost (seeking protection, masculine attention) all that time, and had unknowingly left his fear-frozen aunt behind, at the mercy of the killer-ghost (who found her and threw her over the railing while re-enacting his crime).
...But that would've been too violent for the original audience, probably, and maybe it's not any better than the real ending. I've just gotten used to twist endings in this kind of story. You come to expect them, after a while.