Any star in our own galaxy is no more than about 100,000 light-years away. Since most stars live for millions or billions of years, the odds of any given star having died in the time it took for its light to reach us are very slim. In most cases, as Warrick's answer points out, the odds are practically zero; Sun-like stars, for example, aren't massive enough to go supernova. It's conceivable that something bad has happened to Alpha Centauri A (4.3 light-years away) in the last 4 years, but there's no known mechanism that would cause it to explode.
The most likely candidate in our galaxy for a relatively nearby star that might have exploded is probably Betelgeuse -- but even it's only about 640 light-years away, and could last another million years, so the odds of it having exploded by now are somewhere around 0.1%. Eta Carinae might be another possible candidate.
There's a supernova in our galaxy roughly once every 50 years (yes, that means we're overdue). Assuming that the average star in the Milky Way is 30,000 light years away (the distance to the core), there are probably about 600 stars in the Milky Way that have already gone supernova, but for which the light from the explosion is still in transit. (That's a very rough estimate.) Probably most of those stars have never been seen individually, even with a telescope. On the other hand, stars that can go supernova tend to be large and bright. It would be interesting to estimate how many of those 600 or so stars have actually been seen; I lack the information to do the calculation.
For stars in other galaxies, the story is nearly the same. Andromeda (M31) is about 2 million light-years away; there are probably some visible stars there that have exploded in the last 2 million years (especially since brighter stars are more likely to do so), but the vast majority are probably still as stable now as they were 2 million years ago.
As you look at more distant galaxies, you're looking further into the past, but it also becomes more difficult to resolve individual stars.
The progenitor star for Supernova 1987a, called Sanduleak -69° 202, was discovered before it exploded, so there's at least one case where we were able (before 1987) to see a star that had already gone supernova.
But stars that explode, even in a supernova explosion, do not simply cease to exist. A remnant of the original star remains, typically as a neutron star or black hole.
Finally, there's a famous Hubble photograph of a formation (not a star) called the Pillars of Creation, part of the Eagle Nebula. The Pillars are about 7000 light-years away, but they are believed to have been destroyed 6000 years ago by the shock wave from a supernova. UPDATE : This interpretation has been disputed; see the linked Wikipedia article for details.