Last night, while B. and I were playing a board game, our cat Scully leapt suddenly and violently out of her basket, looking terrified. We assumed she'd had a nightmare (we're fairly sure that both cats experience something like dreaming, although at what level it's difficult to tell), but she spent the rest of the evening very unhappy.
This morning she was still spooked, refusing to be stroked, cowering when she walked and hiding behind things. She's started calming down a bit now (and a phone call to the vet established that there's probably nothing physically wrong), but she's still quite nervous.
This spontaneous reaction of terror to something non-existent sounds a lot like the behaviour of animals which pet-owners describe when they suspect their houses are haunted. I'm not a believer in ghosts (see footnote  for a more nuanced statement about this), and we've lived here for over three years without encountering anything else out of the ordinary. In any case, Mulder remains completely at ease. Which makes me suspect what these owners are describing is, in fact, an unusual but mundane cat behaviour.
What's odd -- and might well strike a cat-owner as evidence of something quite out of the ordinary -- is that it's so out of character. Scully doesn't get this upset when something traumatic has actually happened, like going to the vet's. She's normally self-confident, vocal and demanding of attention to an extent that borders on the tyrannical. Whatever it was the poor love thinks happened, it must have been terribly distressing.
 When I say I don't believe in ghosts, I'm not professing a strong disbelief in them. I do disbelieve, on theological as well as common-sense grounds, that spirits of the dead wander the Earth seeking closure with their children or hiding other people's socks, but I'm open to the idea that some of the phenomena which have been labelled as ghosts have an objective existence.
They may be as-yet-unrealised products of known scientific laws, or result from causes science has yet to categorise. There's an outside chance they may be symptoms of a large-scale seam of irrationality in the universe which science as currently constituted wouldn't be equipped to cover. However, Occam's Razor means I'm hardly going to adduce as-yet-unknown phenomena to explain something which, however unexpected, is explicable by a known and loved cat suddenly going a bit dappy.