Ok, here's some numbers: nuclear power plant core damage frequency is usually estimated at around 5x10^-5 /year, on one accident every 20,000 years. Some estimates from manufacturers for newer designs are much better than that, getting as low as 3x10^-8 /year. Doesn't sound bad, does it? These are risks, I believe, calculated for equipment failure, not human error.
Declaration of bias: I'll henceforth use the number given by regulators, rather than that given by manufacturers. I'm not presenting an exact calculation, just a rough estimate based on publicly available numbers.
So, one accident every 20,000 years. Per plant. There are now worldwide 440 commercial power plants. That's one accident every 40 years. If you include research reactors and nuclear ships and submarines, that roughly doubles the numbers. There's an additional 60 nuclear power plants under construction, 150 planned and 320 under proposal. So in the foreseeable future, we can expect somewhere in the region of 1500 nuclear reactors. One accident every 14 years or so.
Conclusion: nuclear power plants, individually, are safe. The one in your neighbourhood will typically have an accident every 20,000 years, nothing to worry about unless you have a tendency to be paranoid. Worldwide, you can expect a future with a nuclear accident or two per generation. Acceptable risk? Not for me, thanks.
I first did this calculation yesterday. Up to then, I was inclined to think of nuclear power as a minor risk, and of the anti-nuclear crowd has mostly people afraid of something they don't understand, and reacting out of that fear. Now, I'm firmly on the anti-nuclear side.
(Risk is calculated as follows: for a risk of p per plant and n plants, combined risk is not n*p, but rather p*sum(1-p)^i, from i=0..n-1; the calculation is left as an exercise for the reader. The difference is small for n<<1/p, as in this case)