There are 435 nuclear power plants world-wide in over 35 different countries. There have been 3 mishaps over the years. One was Three Mile Island where the safety measures came into effect and prevented any loss of life whatsoever (exactly as they are supposed to). Another was Chernobyl which was an innevitable result of bad managment, design, and secrecy at the hands of a communist government with no regard for human life or safety. Another was ***ushima in Japan which was a tragedy, and the most important to the anti-nuclear energy argument, but it could have likely been prevented had the NISA realized the threat of a large tsunami sticking. (considering the region they are in they should have)
As of the possibility of a nuclear reactor exploding I will simply state that that is not possible. I don't care to list all the facts behind this justification but I will leave a link at the bottom of this post to a site that explains it perfectly. Most people hear meltdown and they think explosion. That is simply not the case. In all regards Meltdowns, given the correct safety measures, are far more controllable and stoppable.
http://io9.com/5782349/why-a-nuclear-reactor-will-never-become-a-bomb