We examine the possibility that a nearby supernova explosion could have caused one or more of the mass extinctions identified by paleontologists. We discuss the possible rate of such events in the light of the recent suggested identification of Geminga as a supernova remnant less than 100 parsec (pc) away and the discovery of a millisecond pulsar about 150 pc away and observations of SN 1987A. The fluxes of γ-radiation and charged cosmic rays on the Earth are estimated, and their effects on the Earth's ozone layer are discussed. A supernova explosion of the order of 10 pc away could be expected as often as every few hundred million years and could destroy the ozone layer for hundreds of years, letting in potentially lethal solar ultraviolet radiation. In addition to effects on land ecology, this could entail mass destruction of plankton and reef communities, with disastrous consequences for marine life as well. A supernova extinction should be distinguishable from a meteorite impact such as the one that presumably killed the dinosaurs at the "KT boundary." The recent argument that the KT event was exceedingly large and thus quite rare supports the need for other catastrophic events.