I have been reading a little bit about nuclear plant safety. I'll just summarize what I learned.
The plants in danger in Fukushima are said to be second-generation, as they were built 40 years ago during the 70s using the technology that time. They are more properly engineered than the one that exploded in Chernobyl in 1986, in the sense that they have more security and safety features in place. A source said they were engineered to withstand strong earthquakes (8.0 or 9.0 I think).
When the 8.9 earthquake struck, sensors in the plants detected it and automatically shut down the reactors. (This is one primary safety feature not found in the Chernobyl one, preventing from a devastating explosion.) However this automatic shutdown does not mean that fission in the reactors immediately stopped. Fission would still go on for some time (not sure for how long) which would need cooling to prevent overheating. There were actually backup diesel generators (I think these were for pumping water) to provide cooling for hours in case electricity went out. But unfortunately for Japan, the tsunami also destroyed these diesel generators and cut out the electricity for too long. (It was like a chain elemental combo.)
And so, as we know, there were already at least three explosions, which were allegedly hydrogen explosions due to high pressure water vapor. These water vapor were coolants (I think), and were contaminated with radioactivity.
From what I undertand, the container vessel of a reactor is supposed to guard against a meltdown and is supposed to withstand a theoretical maximum temperature and pressure of the reaction inside, preventing radioactivity from going out. Unfortunately, the third explosion reportedly damaged the container vessel of reactor 2.
As a last resort, engineers are currently risking their lives from the high dosage of radiation, pumping boron-rich seawater into the reactors to serve as coolant. The boron in seawater is supposed to slowdown the rate of fission.
Based on this, they say that it is extreme bad luck - massive failure in all systems all at the same time, which was not considered when the plants were built.
Nations with nuclear plants are now reassessing the safety of their own plants and nuclear policies.