Another benefit that, if it's been listed, I haven't noticed in this thread: People who work out regularly tend to be in a generally better mood than people who don't. A good workout releases endorphins.
Also, as stonewall50 noted, workouts help release and deal with stress. This also goes a long way toward improving overall mood.
I noticed, as a flight instructor back in the '90s, that students who remained physically active (gym, sports, outdoor hobbies) tended to perform better in the flight syllabus than did the students who locked themselves in a study area and remained generally tense. So, subjectively, physical activity in a completely unrelated area still seemed to bear on performance - most likely due to lowered overall stress levels.