I would say the biggest benefit is my mental health. I have suffered from depression and addiction (thankfully the addiction is in my past now) and habitually turned to food to comfort myself. Since running, I don't feel the need to do that anymore. I honestly don't know why that is but the healthier attitude to food came soon after I began running, maybe because I don't feel as guilty to eating certain foods, so am not driven to binge on them?
Running doesn't give me the 'high' I've sometimes read about but it does give me a perky sense of well being for the rest of the morning which helps my day go better overall.
The other thing it's given me is a greater sense of BEING in my body. Because of my depression and eating issues, I guess I used to regard my body and mind as separate and in some way in conflict. Now, because of exercise, I feel much more integrated and at home in my body if that makes sense. I feel much more like my body is me. Also more body confidence, I haven't exactly got a model figure and I used to be quite clumsy but now I feel like my posture is better and I walk and stand better in general?
Finally, my overall fitness is definitely improving. I don't measure it through any statistics but I can just tell. When I first started running it would take ages for my breathing to go back to normal, now it happens almost at once. I used to be wiped out for about 3 hours after the run, now I still feel tired, but not physically in pain or wiped out. And I do feel more alert than I used to be, mentally, I think (might just be imagining that though).
Finally, I run in a park at dawn and I do get a real sense of happiness from seeing the trees and the sun rising, seeing the seasons change. It makes me feel 'at home' somehow, it's reminded me that humans are meant to be outside and moving and not just sitting down in front of a screen all the time.
I hope that helps :-)