Assume for the moment that ghosts are real, in the sense that they represent an anomalous, paranormal phenomenon (or at least some of them do). As with UFOs, that begs the question: what are they?
Again, as with UFOs, there may well be myriad answers. The one that most people latch onto right off the bat is that ghosts are the spirits of deceased people who remain in touch, somehow, with our plane of existence. The other popular answer that I hear most often is that what we think of as ghosts are, in at least some cases, demons of some sort.
Perhaps. But what if ghosts are something else? Could it be possible that what we see or experience as a ghost represents a break in the continuum of time? In other words, if we view time as not a linear construct, but rather a wave, or even a loop, could we be looking backwards (or perhaps even forwards) in time when we observe a ghost, or similar phenomena? The person we see or experience, assuming that they are from the past, is in all likelihood dead (although if it's the recent past they may well still be alive, in our time), but as we observe them it is as if through a portal, fleeting though it may be, to the past - in short, they are still alive when we are looking at them, at least in their time.
This strikes me as just as plausible an answer for ghosts than the "spirits of the dead" idea (although the two are not necessarily mutually exclusive). Religious scholars have always spoken about some manifestation of an "eternal now" (Henry Alline, who I studied in college, was one; Paul Tillich was another - see here). Scientists now openly speculate that human-initiated time travel in some form or another might be possible. But what if the "time travel" is occurring naturally, as opposed to the human-created forms we usually dream about?
Maybe, just maybe, when we see a manifestation of someone dressed as if they were in the 1890s, they really are still in the 1890s... even as they are, for a moment in time, also in 2009.