Well, the closest star which is going to go any time soon is Betelgeuse, at approximately 800 light years-- We expect to see it go sometime in the next milennium (which, of course, means that it’s probably already exploded, and we just don’t know it yet). It’s unknown how much effect this would have on us, but at the very least, we’d get a lot of light from it: It should be brighter than the full moon, and with all that magnitude concentrated into a point source in the sky, it’d probably be painful to look at directly. X-ray and gamma radiation probably wouldn’t be too severe, but the shockwave might cause problems (yes, in space, you really can hear screams, if they’re loud enough, like a dying star. No vacuum is perfect). Don’t worry too much, though, because the shockwave will travel at considerably less than light speed, so we’ll have plenty of advance warning to figure out something to do about it.
If you really want to worry about death from above, think gamma ray bursters, not supernovae. One going off close enough to Earth would be quite sufficient to sterilize everything in sight, and we probably wouldn’t be able to see the progenitor of a burster very far in advance, so there just might be one close enough that we don’t know about. On the other hand, gamma ray bursts are very short-lived, lasting a few seconds at most, so it’d only sterilize the half of the planet which happened to be facing in that direction.