River Goddess Pantheon: +1 Amenity for cities which have a Holy Site District near a River.
Rivers are invaluable for city settlement, as they supply fresh water and enable the Water Mill (and various wonders) to be built. With it, any city may get a good start at growing and producing as early as the Ancient Era! An Aqueduct built next to it will also supply a nearby city with Fresh Water for Housing purposes.
But rivers do more than that. They provide a bulwark against invasions for any commander that knows how to use them; they turn Deserts into paradise by enabling the Floodplains feature; elsewhere they allow improved farming with the Civil Engineering Civic; they improve commerce thanks to the additional transport opportunities they provide for merchants.
Finally, you may use a River as means of finding the nearest sea in your early exploration. Every river flows from its source to either another river, or to a large body of water - just follow the flow direction.