Nuclear accidents have happened and can happen at any nuclear site. Chernobyl, Three Mile Island, and Fukushima are all prime examples of accidental nuclear mishaps. Even the most redundant of safety precautions can be compromised, and in the worst cases cause a nuclear meltdown. It is important to know your proximity to nuclear power plants and prevalent winds for your area as well, since nuclear fallout can easily travel hundreds of miles through the atmosphere.
Image: Licensed plants in the US in 2008. The regions shown are the jurisdictions of the Nuclear Regulatory Commission. Nuclear plants are not the only possibility of nuclear accident with Department of Defense nuclear assets unaccounted for in this map.