Although you cannot store energy in chemical form in water, energy is and can be stored in other forms in water, some of which are currently being commercially exploited.
Nuclear energy - Undoubtedly some readers are eager to state that water is a fuel if you consider nuclear processes and, of course, they are correct. However, the term fuel, as commonly used, refers to the storage of chemical energy and, in the context of processes involving water and hydrogen gas, the definition refers to chemical energy. Whereas chemical energy is stored in molecular bonds, nuclear energy is stored in the mass of subatomic particles. Haven gotten that technicality out of the way, there is a tremendous amount of nuclear energy stored in water.
In general, nuclear energy can be obtained from either fission, fusion, or radioactive decay processes. We know this because we have used Einstein's famous equation (E = mc2) to demonstrate it. We know how, in principle, to extract nuclear energy from some of the hydrogen atoms contained in water using nuclear fusion. However, doing this in a practical manner is still many years away.
Gravitational potential energy - Energy can be stored in water by raising its gravitational potential, that is, moving it to a higher elevation. This is done naturally when the sun evaporates water and forms clouds, which then condense as rain and deposit the water on the ground at a higher elevation, where it can run downhill and be stored behind a dam. It can also me accomplished simply by providing energy to pump water uphill, referred to as pumped storage. This potential energy can then be tapped by providing a path for the water to flow to a lower elevation (lower gravitational potential), thus converting its potential energy into kinetic energy; then through a turbine, which converts its kinetic energy into electrical energy.
Kinetic energy - The kinetic energy in flowing water is available from several sources:
Free running streams: Original source is the sun. Can be tapped with a turbine or waterwheel.
Flow beneath the floodgate of a dam: Original source is the sun or pumped storage.
Tidal flow: Original source is primarily the kinetic energy of the earth rotating on its axis within the gravitational field of the moon.
Wave action: Original source is the sun. The sun heats water, air, and land. Ocean currents form and weather happens.
Heat energy - Geothermal mining extracts heat energy directly from the earth (volcanic processes, etc.). Electric powered heat pumps extract heat from water or ground that is not necessarily "hot". Today many homes use heat pumps to extract heat from either cold well water or water circulated through pipes buried in the ground where temperatures are fairly constant. The original source of this heat can be man made (as in heat stored in the cooling water from an industrial process), solar, or, as is the case in geothermal mining, the heat stored in the Earth resulting from radioactive decay and the gravitational compression when the Earth was formed.