There are several supernovae per century in our Galaxy, as large stars run out of fuel, and collase in a violent explosion. It is fairly easy to see that on average, every few hundred million years, we are likely to have one go off within 25-30 light years. Previous work has suggested that an explosion this close could be disastrous for the Earth. Many of the damage mechanisms are similar to those for a Gamma-Ray Burst at a much larger distance, and we refer you to that section for some discussion of the damage mechanisms.
While cosmic rays (atomic nuclei moving at high speeds) are a possible impact for GRBs, they are virtually certain to be a major effect of a nearby supernova. All the previous treatments of the effects of cosmic rays from supernova and other high-energy sources have only been approximate. We are now engaged in detailed computations of the energy deposition of high-energy cosmic rays in the Earth's atmosphere, with a grant of supercomputer time funded by NSF. In the near future, we expect to be able to describe these effects in much more detail.
Meantime, collaborator Brian Fields has already predicted evidence--which has been found--of supernova residue on the Earth, and has studied the interaction of a supernova "blast shell" with our Solar System. See When Stars Attack Here is one of his movies.
We've begun our exploration of supernovae by examining the effects of one which might go off soon-- it's called Eta Carinae. Non-technical accounts of the work can be read in Space.com and FauxNews.com. (We regret that MSNBC has not covered this work.)