I'm strangely skeptical of such things for a religious person, and I don't generally believe in such things. That said, I've heard a few credible stories and seen a couple of strange things. I'm not sure how much would be supernatural vs. simply unknown to our current sciences.
For example, in my neck of the woods, we have these "crawlers." Their bodies are about the size of a German shepherd, but with weird, long legs, no fur, and rodent like heads. Nobody's shot one yet to bring back the body, but I've seen them as have a lot of locals. I'm not sure if that qualifies as supernatural though, they're probably just some unknown beastie.