The major benefit of nuclear energy is that it produces energy without emitting any greenhouse gasses. In today's world, where we are so concerned about climate change, this is a very important benefit.
However, nuclear energy is dangerous as well. All we have to do is look at the impact of the disaster in Japan to see that an accident at a nuclear power plant can be devastating. There is also the need to find a way to dispose of the spent nuclear fuel. Finally, you could argue that more nuclear power means more potential for nuclear material to fall into the hands of terrorists.
All in all, then, nuclear power is a trade off; no greenhouse gasses, but much more danger of catastrophe.