Our heads are equipped with two sets of eyes, and, surprisingly, they can work pretty well independently of each other. What I mean is that when shooting, use both of those eyes to survey your scene.
Most of us look through the viewfinder with one eye - for me it is the right eye. But put the other eye to use by glancing up once in a while and seeing what is going on in the scene beyond the borders of the viewfinder.
For example, I recently visited Yellowstone National Park. May and June are wonderful months to be in this amazing location. I was photographing a family of black bears - a sow and her three one-year old cubs. While watching one of the cubs through the view finder I would occasionally look up to see what the siblings were up to in the nearby meadow. With three little ones running around there was always something going on with them.
Of course you have to be wary of missing the shot you are waiting for while looking through your viewfinder. And this technique is also a great way to stay safe.
While photographing a bull elk during the rut I had been so focused on watching him through the viewfinder that I didn't keep surveying my surroundings with my other eye. If I had, I would have realized the reason for why I could no longer fit his antlers in my shot - he was approaching, and close. At the last minute I looked up with my other eye to see this beautiful bull almost breathing down my lens. Not something you want to do any time of year, but especially not during the rut when their hormones are running hot.