The absolute most sustainable heat sources are sunlight and waste heat from your body and the appliances you are already using. However, unless you have the resources to build to passivhaus standards, these won't be your primary heat sources in the winter.
Geothermal heat systems (not to be confused with ground source heat pumps) also take advantage of naturally-available heat, but they are only possible near certain geologic features.
After that, the next most sustainable options are probably in-floor systems using solar-heated water and heat pumps (air-source and ground-source are the most common varieties). Solar water heat generally requires a back-up heat source in cloudy climates and at extreme latitudes, but it might be a good option for cold but sunny regions. Such systems typically require electric pumps to circulate the water through tubing in the floor. Heat pumps also run on electricity, so you can power them using clean sources, but even if you are using grid power from a coal-fired plant, heat pumps are more fuel-efficient than electric resistance heating or even many combustion furnaces. While high-efficiency furnaces compete well with heat pumps for fuel efficiency, they can't take advantage of clean energy sources like the sun or wind.
 Clarification: If 25% of the energy from the fuel makes it to your home as electricity, a heat pump with a coefficient of performance of just 2.5 will be more fuel efficient than a 70% efficient furnace in perfect condition. A COP of 3 will compete with or beat an 80% efficient furnace with a duct system for fuel efficiency. This doesn't account for differences in fuel (coal vs. fuel oil or natural gas), but it also assumes that the furnace is operating at its rated efficiency which is often not true.