Indeed, the chances of another star's supernova (what a stellar "explosion" is called when the star ends its life in a spectacular way) incinerating our planet is tiny. However, if a nearby (meaning in our own galaxy and more like in our immediate neighborhood) supernova occurred, our solar system could get an (un)healthy dose of radiation. The chances are small, but should something like that occur (and it would be very difficult to predict), it could, in fact, have pretty bad consequences for life if the dose of radiation was very strong.
For life-consequences with higher probabilities, see the thread on global warming. In addition, one thing that many people are working on are asteroid-type objects whose orbits bring them very close to Earth. A collision with something like that is what we believe brought the dinosaurs to an end. There is a small chance of such a thing happening again, and it's a bigger chance than a nearby supernova. Take a look at
http://neo.jpl.nasa.gov/neo/ if you're interested in Near Earth Objects.