In general, the existence of supernovae is crucial for life on Earth, as we and our planet are mostly made of heavy elements (e.g., carbon, oxygen, iron) which are forged in the nuclear furnaces of massive stars and then ejected in supernova explosions. The very presence of heavy elements in the solar system thus indicates that generations of supernovae occured before the birth of the solar system 4.5 billion years ago, and made our lives possible. In this sense, supernovae are an essential prerequisite for biology, terrestrial or otherwise.
On the other hand, near-Earth supernovae after the birth of the solar system are at best a mixed blessing if not downright dangerous. The tremendous energy released in the explosion can drastically affect the Earth's biosphere, provided the explosion is close enough. The main impact comes from the ionizing radiation released by the explosion--ultraviolet, X-ray, and gamma-ray photons, as well as a subsequent irradiation by high-energy charged particles (cosmic rays) as the blast wave approaches the earth. The Earth's atmosphere shields us from the direct effects of this radiation, but itself suffers grevious damage through a chain of chemical reactions which result in damage to the ozone layer in the upper atmosphere. Without the ozone to protect us from ultraviolet radiation, the Sun then becomes the agent of death, being particularly damaging to small, vulnerable organisms at the bottom of the food chain. Their demise then propagates to more complex organisms, leading to a mass extinction. It is also possible that the additional radiation could also provoke higher than normal genetic mutation rates. Most such mutations would be either benign or disadvantageous, but a few might be beneficial, and in this respect a supernova could act as an enegine for evolutionary change.
How serious a threat do supernovae pose to us today? Fortunately for us, supernovae are rare on human timescales; no supernovae have been seen in our Galaxy for more than 200 years. Even more fortunately, supernovae near enough to be a threat are much rarer still. For example, the massive stars that are doomed to die as supernovae are also the most luminous stars during their lives. This make these stars the easiest to spot, and we have a complete catalog of all of the massive stars nearby, and there are none anywhere close enough to currently threaten the Earth. So there is no need to lose sleep over a supernova threat today!
However, over the whole history of the Earth, millions of these explosions have occurred in our Galaxy. It is very likely that a few of these occurred very near the Earth. guaranteed that such events have occured, on average about once per 200 million years. While this is an enormously long time, it implies that dozens of supernovae have exploded within the "kill radius" over the life of the Earth. Even so, the most recent nearby event likely occurred millions of years ago, beyond human memory and probably before humankind.
The danger posed by nearby supernovae has consequences not only for the past (and future!) of life on Earth, but indeed for the development of life throught our Milky Way Galaxy. The possibility that other star systems in our Galaxy can foster and sustain life is now emerging as a question that science can begin to address meaningfully, and is a central defining question in the new field of exobiology.
The frequency of supernova explosions is a key factor in considerations of the "Galactic habitable zone" -- the prime real estate of our Galaxy thought to be the most hospitable for life. Key to current thinking is the double-edged influence of supernovae on life. Since supernovae provide the heavy elements needed as raw materials for planets and life, the metal-poor (and hence supernova-deficient) outermost regions of our Galaxy are thought to be unfavorable environments for formation of life-bearing stars. On the other hand, the innermost regions of our Galaxy are so densely packed with stars that there are plenty of heavy elements, but the rate of supernova explosions is much higher than here; for this reason, the Galactic center and environs may be to