Phil Plait reports that, contrary to popular belief, most of the 6,000 stars visible from Earth are still burning strong:
Even the most luminous stars, which use up their core fuel far more quickly, can live for 1 million years or more. That means the odds of a star happening to die while its light is already on its way to Earth are very small; in terms of the star’s lifetime, a few thousand years is the blink of an eye. A star would have to be very, very near its own death for this to happen after a very, very long life.
I can think of very few exceptions, though Eta Carinae fits the bill. It’s on the edge of exploding; in the 1840s it underwent a massive paroxysm that was just short of a supernova event. It may not go off for another 50,000 years, but it might tonight. And at a distance of less than 10,000 light years, those are not terrible odds that, in a sense, it’s already gone and we just don’t know it yet. But that’s the exception, with the vast majority of stars still merrily fusing away, lighting up the galaxy.