Running means different things to different people: competition, a way to fend off some weight, a social activity, even transportation. While I do frequently enjoy these aspects of running, the reason I keep doing it is for the mental benefits.
I prefer running alone, I prefer trail running over road running, and I don't like listening to music during runs. This allows me to truly escape from all the distractions that constantly fight for my attention, to allow my thoughts of the day to slip away, and to focus just on the rhythmic 'tsh-tsh-tsh-tsh' of my feet on the dirt.
Once I get settled into a good pace, my creative mind begins to wander.
The endorphins of a hard climb and the feeling of awe from scenic views seem to have a guiding effect on my wandering, toward positive, self-reflective, innovative thoughts. I don't mean to romanticize trail running over other activities. Surely other activities consisting of repetitive physical exercise, such are cycling, rowing, or swimming, can result in similar states of mind. Trail running is simply the activity I've found to be perfect for my physical and mental state and I encourage you to seek out yours.
I now rarely finish a run without a thought or idea I want to quickly write down to further explore later. Of course they aren't all winners, but innovation is often harder to grasp the more you reach for it. Trail running is one of the ways that I've discovered can, almost automatically, jump-start my innovative thinking.