The Renewable-Energy tag here covers questions about the physics (not the politics or economics) of energy sources that do not rely on the consumption of an exhaustible fuel. Tidal, geothermal, and the direct and indirect solar energies (direct: photovoltaics, CSP, solar thermal; indirect: wind, wave, biomass) are renewable energy.
There is also an Area51 proposal for a new StackExchange Q&A site dedicated to renewable energy:
Biomass for heat is probably as old as human civilisation; more recently, biomass is used for biofuel in transport, for biogas in heating, or for burning and driving a turbine to provide electricity. All of these sources combined make biomass the world's largest source of renewable energy.
Currently, the world's dominant source of renewable electricity, hydro-electric can come in several forms: run-of-river; storage hydro; and pumped-storage hydro. The latter is a form of energy storage rather than generation, but is nevertheless typically classified as renewable energy.
Originally used for grinding grain, now more commonly used for generating electricity in turbines
The direct conversion of sunlight into electricity.
The extraction of underground heat for space and water heating goes back many centuries; more recently, the heat has been used to drive turbines to generate electricity.
Capturing sunlight for heating water (and occasionally for space-heating)
Concentrated Solar Power [CSP] Concentrating sunlight onto a fluid which is then used to drive a turbine or Stirling engine.
Full-scale commercial grid prototypes:
The movement of waves is harnessed either through hydraulics or to drive turbines, to generate electricity.
Converting kinetic energy from daily / twice-daily tidal movements, with underwater turbines.
Generating electricity from salinity gradients. The first prototype went in the water in Norway, in 2009.
Building novel synthetic living photosynthesisers from basic genetic building blocks; or novel catalysts to harness sunlight to release hydrogen from water; various labs are working on different routes.
Tidal benthic friction
The hypothesis is that tidal water movements are mostly dissipated as friction against the bottom of the sea, and that by placing energy harvesters on the seabed, the kinetic energy can be converted to electricity. Specific harvesting technologies, scale of the resource, and the impact on benthic ecology, are currently unknown.