As a child, my yard butted up to a cemetery. I was in there all of the time. I never saw anything out of the ordinary, although I did hear a fox "screaming" out there at about three in the morning. It certainly startled my out of my sleep.
Another time, in a nearby cemetery, I encountered a great horned owl doing some tree-hopping. If one didn't know what it was, it would probably be frightening.
There was one time, though:
When I was on night shift, we would patrol one cemetery that was right in the middle of the ghetto (Woodland Cemetery). It is actually a very interesting cemetery, dating back to the mid 1800s, and being home to many ornate mausoleums, and towering memorials, many featuring marble angels. One rainy night, a shadowy figure emerged from amongst the crypts, and started making its way toward our car. It slowly ambled toward the small road that bisected the cemetery, twitching and limping along. Finally, it revealed itself under the pale glow of the only working light in the cemetery.
It was...
...a cracked-out prostitute taking a shortcut to her housing project.