What constitutes the most serious type of accident which could occur at a nuclear power plant?

The most serious type of accident which could occur at a nuclear power plant is core meltdown caused by a failure of water to circulate among the fuel rods.

This is what happened in F. ukushima, Japan, in 2011, after a series of devastating earthquakes and tsunamis. This is why F. ukushima is still experiencing extremely high levels of radiation and parts of that area cannot be inhabited anymore.