The reactors currently at risk in Fukushima were built in the 1970's as Boiling Water Reactors (BWR). These need a pump to move water around the fuel rods, which act like the element in the bottom of a kettle - in order to create steam to drive the turbines, which make electricity. Also, the water helps to keep them cool.
When the earthquake occurred, this stopped. Diesel generators which would normally provide back up failed due to the tsunami wave. This led to an increase in temperature - causing the remaining water to evaporate, releasing hydrogen which caused the explosion at the #1 reactor.
This has led to people questioning the idea of building nuclear power stations in areas prone to earthquakes. However, those in favour of nuclear power state that new generation reactors are self servicing and do not need a pump to move water around. This means that if the circumstances were repeated near this type of reactor, it would be able to keep going without the risk of overheating and meltdown.
For more detail about the nuclear reactors at Fukushima and the risks involved click here via the BBC News website.
For the main arguments about nuclear power, read this article in the Independent from 2005. It outlines the top 5 reasons for and against this form of energy generation.