The link between exercise and health wasn't known for certain until 1949, when Jerry Morris noticed that bus-drivers had more heart disease than bus conductors. After a study of 31,000 people, he concluded that there was a 0.27% chance per year of coronary heart disease for drivers, vs 0.19% for conductors. The size of the sample was large enough that there was little chance this was coincidence.
While it may seem obvious to us today that there is a link between exercise and health, it's not as intuitive as is seems. Healthy people can drop dead of a heart attack in moments while so-called unfit "couch potatoes" will survive decade after decade.
A person who does a little exercise (less than 75 minutes per week) has a 20% lower mortality risk than a person who does none. Doing the minimum 75 minutes of exercise recommended by the US Physical Activities Guideline 2008 lowers your mortality by 31%. 150 minutes gets you 37%.
The improvement peaks at about 40% for 22 hours of exercise so it's probably not worth going that far. In fact, exercising too much can start to undo the health improvements and cause problems.
Some studies suggest that too much exercise can actually be bad for you. You have probably heard of runners dying of heart attacks in the middle of races. It was found in a study of 10.9 million runners that the incidence of actual fatalities (42) is actually very low, and a study of 52,000 people done over 15 years showed that running a little was better than not running at all (19% lower mortality), however, it also found that running too much actually increases your mortality.
Running more than 32km per week, faster than 11kph, or more than 5 times per week does not improve your health, and may damage it instead (musculoskeletal trauma, metabolic derangements, CV stress).