There are cougars and black bears, depending on where you hike. They usually turn tale and run if they see you.

Mostly I would be worried that you got hurt and nobody knew where to find you. When I was in college a guy broke his leg badly mountain biking not far from the college. Then died of hyperthermia over the night. He wasn't far from the dorms.

Bring a little backpack with a couple emergency blankets and a heavy sweatshirt.