Physical Fitness and Personality
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 (HIIT) - sprint till winded, recovery walk, repeat until exhaustion. (source) (source 2). I find it far quicker and more beneficial than endurance running.
Update: I think I can finally explain why interval/hiit/sprint training is the most effective way to exercise. Basically, you can only sustain max running speed (and likely max intensity at any exercise) for 30-35s (200m-400m) due to your muscles reaching peak lactate acid levels (source) (source 2). So, by exercising in @30s peak intervals (with 30-60s rest breaks) for as long as you can, you effectively max out your anaerobic/strength and your aerobic/endurance systems. This also explains why runners in events longer than 400m look so muscle wasted and wiry. Training beyond 400m intensely causes you to over-develop your aerobic system (endurance) at the cost of your anaerobic system (strength). All the recent exercise systems p90x, Insanity, etc. work on the same principle. Except, I think they over complicate things (and don't accommodate well for the natural range in each beginner's athletic ability). If you max out your lactate/anaerobic and aerobic systems, it's going to cause your whole body to restructure/rebuild, regardless of what muscle groups you use to max it out. Sprinting is most effective because your legs are your largest peripheral muscle group. I'm also cynical of the common advice to only do HIIT every other day. I think it can be and should be done every day.