Since United States obviously seriously considers building new nuclear power plants in years to come (even despite the recent nuclear disaster in Japan) I reckon it would be a good idea to discuss the main advantages and disadvantages of nuclear power plants. The most important issue is of course the safety of the new nuclear power plants. When discussing the safety of new nuclear power plants then it's important to say that nuclear power plants have significantly improved their safety in the last few decades which means that nuclear disasters like Chernobyl and Three Miles Island are almost impossible to happen again, though a situation similar to what happened in Japan remains possibility, even with the improved designs and other advanced technological aspects.
All newly built nuclear power plants need to satisfy maximum safety standards, and the newest nuclear reactor designs really ensure maximum safety by applying the concept of the negative feedback loop, which ensures that as the nuclear reactor's power output increases, it becomes more and more harder to squeeze any more power out of it, meaning that nuclear chain reaction that could lead to nuclear reactor explosion is almost impossible to happen. Though this design is not totally foolproof it is much safer compared to the older designs. Of course there are still many older nuclear power plants that still use the older design, but even they ensure the maximum safety as there hasn't been any major accident since Chernobyl.
Nuclear power plants do not need fossil fuels to produce electricity, and this means that they do not release harmful carbon emissions that contribute to pollution and climate change problem. Since there are no carbon emissions nuclear power is also considered clean energy source just like solar, wind or geothermal energy.
In order to properly operate nuclear power plants require nuclear fuel. Nuclear fuel mostly used in nuclear power plants in uranium though some nuclear power plants also use plutonium. Uranium is plentiful in United States, and building more nuclear power plants would therefore contribute to better energy independence as there would be reduced need for importing expensive foreign fuels.
Nuclear power plants operate very efficiently and reliably. Their efficiency is comparable to coal power plants, and once they are built they are extremely reliable given that there's enough uranium to feed them, and as already said there is plenty of uranium in United States.
The main disadvantage of nuclear power plants is no doubt nuclear radioactive waste that has lifespan of more than 5000 years so more new nuclear power plants will mean more radioactive waste, and current nuclear waste storage options definitely do not ensure totally safe storage for the next 5000 years or so.
Another disadvantage are relatively high construction costs, and there is also the high number of licenses that need to be obtained prior and during the construction which significantly prolong construction time but are needed to ensure the maximum safety of new nuclear power plants.
With the increased number of nuclear power plants there would also be the greater possibility of terrorist attacks so nuclear power plants need not only to ensure the maximum safety against nuclear reactor explosion but also against possible terrorist attacks.