Nuclear fission power is one of the cleanest, safest, and most abundant sources of non-renewable power that can be used with today's technology. However, its use has been limited in the United States, only about one-fifth of all power plants in the US are nuclear. The vast majority of plants in the US are coal-fired. The reason for this is primarily political, not technological, because nuclear power has distinct advantages over coal.
Coal plants emit thick clouds of noxious smoke containing black soot, carbon dioxide, carbon monoxide, sulfur dioxide, and nitrogen oxides. All of these components have adverse effects on the environment. Coal mining is also dangerous business, with many people dying or getting injured each year because of mining-related accidents.
Nuclear plants, on the other hand, emit no polluting gases whatsoever. The only thing that comes out of those big cooling towers is steam. Because so little uranium has to be mined to make the same amount of power as coal, there is less chance for uranium mining accidents. When the resources of all possible fissionable material is added up, including thorium and the use of breeder reactor, there is actually more energy contained in nuclear fuel reserves than there is in coal reserves.
Perceived drawbacks of nuclear power include radiation emission, nuclear waste, and meltdowns. Many would be surprised that a coal power plant emits more radiation than a nuclear one! Nuclear plants have concrete shielding more than a meter thick. In a test of the reactor's shielding and strength, testers crashed a jet plane into a nuclear reactor. The plane disintegrated, with barely a dent left in the concrete. Terrorists would be wasting their time messing with nuclear plants. Nuclear waste is stored in shielded containers, so there is no radiation threat in that either. In fact, some nuclear waste can be recycled into nuclear batteries, a lightweight source of portable power.
As for meltdowns, there were two: Chernobylin the USSR and Three Mile Island in the US. The former was terribly designed with few safety measures, while the latter was well designed. The meltdown of the well-designed Three Mile Island plant resulted in no casualties. Chernobyl's meltdown did result in 4000 deaths, but as I said before, Chernobyl had all the safety measures of car with no seatbelts and its brakes cut. When nuclear plants are properly designed, meltdowns do not pose a serious risk.
Thanks to Brontosaurus for the number of deaths caused by Chernobyl