Nuclear, wind, and solar power emit no greenhouse gases (GHG) when operating, but there are life-cycle emissions, in mining and refining uranium, building aluminum frames for photovoltaic (solar) panels, and manufacturing concrete and steel for wind and nuclear power. A life-cycle analysis looks at all of the costs from getting the fuel, construction and decommissioning, transportation, and operation.
Several analyses exist, you can go here to see others. Solar GHG emissions are dropping as technology improves (also true for other electricity sources).
If nuclear electricity (rather than coal electricity) is used for uranium enrichment, nuclear life-cycle emissions drop further.
Wind, solar, and nuclear are the major remaining low GHG sources of electricity, as there are few expansion possibilities for hydroelectric.
For some sources of energy, the major GHG emissions occur in building the plants.
From Per Peterson at UC, Berkeley: Current and Future Activities For Nuclear Energy in the United States:
• Nuclear: 1970′s vintage PWR, 90% capacity factor, 60 year life
— 40 MT steel/MW (average)
— 190 m3 concrete/MW (average)
• Wind: 1990′s vintage, 6.4 m/s average wind speed, 25% capacity factor, 15 year life
— 460 MT steel/MW (average)
— 870 m3 concrete/MW (average)
• Coal: 78% capacity factor, 30 year life
— 98 MT steel/MW (average)
— 160 m3 concrete/MW (average)
• Natural Gas Combined Cycle: 75% capacity factor, 30 year life
— 3.3 MT steel/MW (average)
— 27 m3 concrete/MW (average)
[MT = million metric tonne]
Concrete + steel are >95% of construction inputs, and become more expensive in a carbon-constrained economy.
Because nuclear power operates at 90% capacity, 1 MW/0.9 (1.1 MW) of installed capacity is needed to produce 1 MW power. Similarly for wind, installed capacity must be 1 MW/0.25 (4 MW) to average 1 MW power.
Wind plus natural gas (or other backup power plants) requires natural gas plants to be built. These do not add much GHG compared to the GHG emissions in windmill construction; they are, however, expensive.
For an example of a photovoltaic (solar panel) GHG analysis, see Life Cycle Energy Consumption and GHG Emissions of a Field PV Plant (pdf).
Carbon Capture and Storage
CCS gasifies coal and burns the products in oxygen rather than air, so only 1/5 as much waste gas is produced.
According to Accounting Rules for CO2 Capture and Storage (pdf), more CO2 is stored than would have been emitted without CCS, because so much extra energy is required for the process, about 40%. If only the upstream emissions still exist, GHG emissions from coal would be reduced to between 250 and 430 g CO2/kWh, 40% more than upstreams emissions for current coal use, to account for the extra energy required. This reduces coal GHG emissions below those from natural gas.
Update Some of the upstream costs from coal come from the current mix for electricity, some from natural gas escaping to the atmosphere during coal mining, some other. Reducing fugitive emissions from natural gas and switching to electricity produced by CCS will reduce upstream emissions for coal.