Per watthour, nuclear power is the safest form of energy production, by a very large margin[1].
Chernobyl is the worst nuclear disaster in history. The UNSCEAR report states that 62 deaths can reliably be attributed to the disaster. Peer-reviewed estimates of additional deaths in the long-term range from 6,000 to 50,000.
You mightn't have heard of the Banqiao Dam, but you should have. In 1975, Typhoon Nina destroyed 62 dams in Henan Province, China. The biggest of these, the Banqiao Dam, released 700 million cubic metres of water over the course of six hours. The resulting flood destroyed six million buildings, killed 26,000 people and caused a humanitarian disaster that killed another 145,000.
The business of energy is inherently dangerous. We have an instinctive aversion to radioactivity, because it's strange and invisible, but it's just energy. Someone falling into a nuclear reactor seems inherently more horrible than a solar panel installer falling off a rooftop, but a death is a death. The Chernobyl exclusion zone seems innately more frightening than the beaches cordoned off after the Deepwater Horizon disaster, but cancer from crude oil exposure is still cancer.
We've got very good at controlling the risks of nuclear power. We know what the worst case scenario looks like. Radiation exposure isn't nice, but neither is a mine collapse, a gas explosion or climate change. Stories involving radiation are attention-grabbing, but we can't allow that to distract us from the hard data.
[1] http://nextbigfuture.com/2011/10/snapshot-of-deaths-per-tera...