Nuclear power is controversial for a number of reasons, but as a zero carbon energy source it needs to be discussed soberly in connection with climate change.
It's not zero-carbon, it's low carbon. There exist no zero carbon electricity sources. The iron must be dug from the ground - with drills using oil. It must be roasted with coking coal - a process chemically releasing CO2. It must be melted and alloyed with other things like vanadium for hardening or chromium to make it "stainless". Aluminium for wind turbines must also be dug up and refined, and it's made with huge amounts of electricity. Concrete's materials are likewise dug up and ground up and refined, and the concrete setting chemical process also releases CO2. And then the plants when built have to be maintained with vehicles tooling around, parts replaced and so on.
Hydroelectric's often thought of as low emissions, but in some cases the emissions are even higher than for coal - because they flood a wooded river valley, and all the plant matter rots and releases methane, which is a strong greenhouse gas (at least 23 times stronger than CO2, though some scientists recently are arguing for calling it 32 times or even higher).
The net result is that for each kWh of electricity produced, we get something like,
0.07kgCO2-equivalent = Geothermal, Solar PV, Solar thermal, Wind
0.22kgCO2e = Hydroelectric/kWh
0.44kgCO2e = Nuclear, Landfill gas or Natural gas
1.50kgCO2e = Oil or Coal
Now, some individual power plants are better, and some are much worse; my own state of Victoria's old Hazelwood plant burning brown coal had about twice the emissions of a regular plant. And the French nuclear plants are pretty good, while the Chinese ones are awful in terms of carbon emissions.
There's no such thing as zero emissions. There's just more or less emissions. But again we come to Jeavon's Paradox; halving the emissions from each kWh of electricity may lead to
more electricity use, and thus the emissions don't drop as much as you might expect, or in fact they go up.
In any case, with or without global warming the issue is depleting resources. The oil is going to run short, then the gas, and finally the coal. Some time in the middle the uranium will run short.
We can make the uranium last longer with breeder reactors, but that also makes more plutonium, and going on the Iran and DPRK experience, quite simply the Western world is not going to let the Third World have a stack of plutonium - any solution to the energy and emissions problem must be a
global one, or along with electricity it will generate conflicts. Thorium reactors have some promise, but thorium reactors require a plutonium seed, so that each thorium reactor requires a uranium reactor.
Basically, if we insist on powering our lifestyles by
burning things - whether the burning is combustion or fission - then our lifestyle like those things will be finite.
Consume less. It takes some years and billions of dollars to build new and better power plants, but we can reduce our consumption
now. And again: even if you don't care about the environment or depleting resources, these are all good things to do for our finances and physical health, too. You don't need to be a greenie to think that fresh fruit and vegies and bicycling are better for you and your wallet than takeout and driving.