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For your common garden variety type I and most type II supernovae we should be OK if we are beyond 50 light years of the source.
Some type II supernovae will collapse to form a Kerr type (rotating) black hole which is believed to be the progenitor of GRBs.
As Carl states if we are at or near the line of sight of the axis of rotation of the black hole we could could be in the line of fire of extreme high energy gamma radiation. The "safe" distance would be in the magnitude of thousands of light years.
Our demise would be caused by the destruction of the ozone layer.
When ozone absorbs UV radiation, ozone breaks down into oxygen atoms and molecules. Oxygen atoms being chemically reactive can recombine to form ozone so there is no net loss of ozone.
Gamma radiation on the other hand not only breaks down ozone but strips off the electrons which prevents ozone from reforming.
So if we were able to survive the initial blast of the supernova we will probably end up succumbing to solar radiation and/or the extreme climate change that would occur due to a non existent ozone layer.
Steven
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