Barefoot walking/running, climbing (trees, at rock gyms, outdoors), swimming, fighting (preferably controlled situations such as a martial arts or boxing gym), are all extremely FUN, liberating, invigorating, and "natural".
Just as eating real food (fruits, veg, meat, etc.) satisfies the body's nutritional needs (i.e. fuel), a broad spectrum of movement satisfies our body's need for exercise (i.e. tuning and aligning).
In terms of Pareto's principle (the 80/20) rule, something like Crossfit offers the most bang for the buck. With a somewhat limited number of movements, (squats, Olympic lifts, push-ups/pull-ups, etc.) you can get most of the physical exercise that you need. However, the remaining "long tail" of movement has a cumulative effect that can really add up.
For example, going out and playing a game of tag, climbing a tree, getting into a friendly tussle, hopping from rock to rock down a river, etc. offers millions of subtle variations, modifications, adjustments, and adaptations. These types of activities cannot be replicated in a gym setting and must take place outside in a natural environment.
It is like comparing watching something on an HD TV vs seeing it with your own eyes. Direct contact with the natural world will always offer than intangible "something more" that we all aspire to.