I used to watch a show called Ghost Hunters on SciFi. They didn't actually look for tiny little things and yell "OMG IT'S A GHOST", they tried to reasonably find ways stuff could be happening without paranormal influence, but on two or three occasions they'd be like "That shit is haunted" when they couldn't explain something. I think the most notable 'proof' they ever got was when they were in a lighthouse or something. One of their members was sitting inside a closed room, only one exit/entrance, on a stool and his camera was on the other side recording everything. Nothing happened for a while, but when he went to the bathroom, the camera recorded the stool sliding across the floor and changing position. Of course, it could have been doctored, but hard to do.
In another episode when they were on a 'haunted' ship, they had set up a camera in one of the 'haunted' bedrooms and they caught the blanket gradually being tugged off the bed by a 'ghost'. Later, though, one of the members noticed that a pillow on the bed suddenly moved between two of the frames, and they figured out how someone had faked the 'falling' blanket by pausing the video, moving it a bit, then resuming play only to pause again, creating a frame-by-frame effect of a ghost moving the sheets. That just shows how a lot of 'proof', even video, of ghosts can be faked.
Does that automatically mean ghosts don't exist? No. I haven't seen concrete proof that they do, but I have seen a few instances of 'ghosts' that can't really be explained, so I'm not going to take on a holier-than-thou mindset and dismiss any potential finding of the supernatural before rationally considering it.
tl;dr: Don't really believe in ghosts, but I'm willing to keep an open mind on the subject of the paranormal.