I think there is a strong link between physical fitness and psychological/physical health (source). Physical attractiveness (body but not face) is also correlated to physical fitness to some degree (source). The more unfit you are the higher your resting heart rate and potential cortisol levels. Cortisol is a fight or flight chemical which if over produced inhibits mental functioning and increases the chance of a heart attack. There are numerous other chemicals that your body over or under produces when you have reduced fitness.

Aerobic/cardiovascular exercise increases slow wave sleep (the deepest, most restorative part of sleep) and heart rate variability (which correlates to reduced mortality risk), anaerobic exercise does not. Running is one of the best cardiovascular exercises. A recent study in the Netherlands found that frequent running reduced mortality by a factor of 3.0 (frequent walking only scored 1.4).

Best type of running? Having spent 7+ years doing endurance (long distance) running, I now prefer sprint training - sprint till winded, recovery walk, repeat until exhaustion. (source) (source 2). I find it far quicker and more beneficial than endurance running.