I don't care for the term "supernatural", as it would literally mean "outside of nature", and that would presume that we know everything there is to know about nature and the universe. Paranormal fits better, because it means "outside of the norm" and humans have a very limited view of what is normal.
As for ghosts and the like, I'm an amateur ghost hunter/urban spelunker in my spare time, and honestly 99.9% of the time, there's a logical, non-paranormal explanation for the "hauntings." It's that .1%, though, that helps me keep an open mind. Everything else, well, I'm a half-gypsy shaman, so I guess it goes without saying that I'm a spiritual person, and I've seen a lot of things over the years that defy rational explanation. So, yeah, I believe in the paranormal, I just don't believe most people about the paranormal.
BTW, I know this is beating a dead horse, but to everyone who says "I've never seen it, so I don't believe in it," I've never seen the Pacific Ocean. Obviously this means it doesn't exist, all the pictures of it are hoaxes, and everyone who claims to have seen it are lying or insane. That makes sense, right? :V