I'll add my experiences as well and let you all decide what to do with it. I've seen two apparitions at the Whaley House, and I've never been able to make heads or tails of what I saw. Although these stories happened some time ago, I've written them down before, so recall isn't an issue here.
The Whaley House, in Old Town San Diego, CA is considered one of the haunted houses in the United States. The Whaley House, a two-story Greek Revival, was built in 1857 on the site of a former gallows (probably because the land was cheap). When the house was built it was (I believe) the largest in the city, serving for a time as the San Diego court house as well as a community theater. Performances could reportedly hold 150 people, which, if you visit the house seems incredible since the theater isn't huge. The original inhabitants of the house (the Whaleys) - back in the 1850s/1860s reported hearing noises/odd things, which they wrote about in their journals. Note this was over 150 years ago. Today the house is said to be haunted by many ghosts, including Yankee Jim (hung on the site of the house in the early 1850s), and the Whaley family.
I've visited the Whaley House three times. My first time visiting the house was in 2005 over the 4th of July holiday with my sister and cousin. This was in the mid-afternoon. We were up in the 2nd-floor theater, while a group of maybe three people were recording the master bedroom hoping to catch something (they said that the master bedroom is supposed to be the most active room in the house). Note that the layout of the 2nd floor has the theater at the end of a hallway by a staircase, and the master bedroom is essentially right across from the theater immediately to the right of the same staircase. The people video recording were getting frustrated that they weren't catching anything and were getting ready to leave. I specifically remember the "ding" from the camera as they turned it off. Not a second later I heard a loud bang come from the master bedroom; the people originally recording immediately ran downstairs and out the house (screaming, of course). After catching up with them afterward I learned that a chair in the back right corner of the room had levitated, spun around (!), and hit the back wall. This was the bang that we heard.
Of course, we were curious what the bang was, so we walked from the theater to the master bedroom. The three of us were the only ones there since the people originally recording had all run downstairs. As soon as we got to the bedroom a full-bodied apparition in 19th-century attire appeared at the site of the chair. It looked just as real as any flesh-and-blood human being, except for the face. The face seemed devoid of features, so that it was more like a characterization of a face than a real face. The rest of the apparition looked completely real, including that it was totally opaque. I could tell it was a man dressed in mid-19th century attire.
This apparition then proceeded to run across the master bedroom, vanishing just before getting to the closet that connects the master bedroom to the theater. While the apparition ran across the room it affected the physical world as though it was a real person. The wind from the apparition running ruffled the window curtains, causing them to billow enough that they ended up in front of (covering) the window lamp. The window was closed. As well, the apparition ruffled the carpet. It was as though the apparition was running so fast away from the site of the chair that it slipped a little on the rug and kicked it slightly back. I saw the apparition affect the physical world in front of me... The ghost was never more than a few feet away. The apparition continued running until reaching the hallway closet that connects with the theater. Immediately before the apparition would have hit the curtain that marks the closet, the apparition completely vanished. When the apparition vanished it was maybe no more than 2 feet away from me. It never noticed the three people looking at it-- the apparition was making a b-line directly for the closet.
Just to make sure I wasn't going crazy, my sister and cousin, who were both there next to me, said that they saw the exact same thing.
Immediately afterward we went downstairs to find the docent. He told us that the person we described (including what they were wearing) matched Yankee Jim, who is known to play pranks and to be active in the master bedroom. The docent told us that the clothes that we described the person as wearing are the same clothes that Yankee Jim is said to have worn the day he was hung. He said that what we saw was one of the most active sightings ever reported in the house and let us all into the master bedroom through the theater.
Nothing in the bedroom was amiss, other than the ruffled window curtain and rug, and there was nothing there that would have been out of place in the 1860s. There were no cameras, light projectors, strings, trap doors- nothing. Just an old bedroom - I can't see any reasonable way for what I saw to be explained. I could say that my senses were lying to me, but I had two other people next to me that saw the exact same thing. Plus even if all our senses were being duped, how could I explain how the physical world (carpet ruffled and curtain moved) was affected?
This docent had us put our experience and names in a book which was kept on the 1st floor of the house, which recorded all paranormal activity.
I visited the house again a few years later and the docent remembered who I was, where I was from, and what I had seen (probably because of that book). I was talking with the docent at the end of the day, and along with the docent was the very last person out of the house as he locked it. I can attest that the house was completely empty. Immediately after leaving the house I was looking up at the 2nd-floor windows and saw somebody walk across. Their top half was well-defined but their bottom half was poorly defined and disappeared a little below the shoulders. Although I'm the only person to see this second ghost I know it wasn't a hallucination. I caught this on video (unfortunately the video is analog and I don't have any analog players at the moment). The house was empty, and as I noted for the master bedroom sighting, there are no projectors or strings or anything of the sort anywhere in the house. A projector system large enough to create what I've seen at the Whaley House (if that would even be possible to project with current technology) would be very prominent when visiting.
I really do believe I've seen one full-bodied and one partial apparition on the 2nd floor of this house. I don't see any other explanation... I think what I saw in the master bedroom is impossible to explain without ghosts. It makes more sense to say that these ghosts operate under the rules of reality and that we just don't know all of the rules, rather than to say these apparitions don't make sense with current scientific knowledge, therefore must not exist. Given that ghosts give off characteristics that can be picked up by electronic equipment (EVPs, thermal phenomena, full-spectrum phenomena, etc) and that various hauntings repeat themselves, I think the phenomena of ghosts is scientifically testable. You just need a good grasp of the scientific method and experimental design. But I digress.
Both sightings were complete accidents... I never intended to see anything nor sought to see anything. I just happened to be in the right place at the right time. Given that Yankee Jim only showed himself when he thought that nobody was looking, I take it that he goes out of his way to stay hidden. It's remarkable to remember though that the Whaleys themselves reported hauntings when they lived there. If Yankee Jim was the ghost the Whaleys were referring to, he's been haunting that house for over 160 years.
I visited the house most recently in 2013 on a guided tour. This was my first time taking a tour- the other times I was allowed to freely explore the house. However, this time I didn't see anything unusual. If the house was installing advanced technology, you would think they would have it do something during their tours when the most people were in the house. But no, nothing. I've only ever seen things when alone or in a small group.
On this latest visit I asked for the book recording paranormal activity in the house but was told no such book existed. I imagine management of the house changed and the book was removed since such a book did exist 10 years ago or so. Do I think the Whaley House is haunted? Yes... The second floor especially.