I sleep fine enough to do what I need to do during the day. But, certainly I'm concerned about bears, and other stuff. Getting struck by lightning, too. Those are probably my two biggest fears.
One time I took my wife into the backcountry of RMNP, she was actually just my gf then and that was how I proposed, on a mountain top. Anyway one time I awoke to a bear sniffing walking through camp and sniffing the outside of the tent. I was petrified, didn't know what to do. I was considering grabbing my knife and charging out and defending us. As I was considering what to do my wife started to stir, and I squeezed her and said "don't move, bear outside." We both quivered with fear for a few minutes as we heard the bear walk, sniff, walk, sniff. Then, after what seemed like an eternity, I realized it wasn't a bear, but just the tag that the NPS makes you put on your tent blowing against the side of the tent in the wind. Relief, embarrassment.