Definitely!
I have had first hand experience. My first apartment was in a really, really old house. It had a ghost with a sense of humor that would open the shower curtain when I wasn't home. Every day, I would make sure it was closed, and sure enough, many times I would return to find it open! This is the same ghost that someone stacked a storage room full of empty boxes into neat little piles after I moved in. As we unpacked the boxes, we tossed them through a window and into this room. The next day, the boxes were a mess when I left the house, and were stacked neatly when I returned. We had changed the lock ourselves, so we knew there was nobody else with a key.
There have been other supernatural experiences, but that first apartment was the spookiest. I didnt' believe in ghosts until then.