Well… EACH AND EVERY STAR in the galaxy and in the collection of galaxies making up the known Universe (or Cosmos, a word I prefer because it sounds cooler) goes through a life. Just like a human being, this life cycle can be thought of as a BIRTH stage, a NORMAL LIFE time stage (for humans its birth till death) and then for stars an END stage.

Now just for some background, in OUR galaxy, the MILKY WAY Galaxy, there are about 300,000,000,000 (three hundred billion) stars. In the cosmos there are about 1 trillion ( 1,000,000,000,000) galaxies. So this means there are about 3,000,000,000,000,000,000,000 STARS in the known Cosmos. That is a very large number!

At any rate, EACH star has its own star life, a normal lifetime shining away at a constant rate for a period of time that depends on the mass of the Star. For the SUN this period is about 10 billion years. As the Sun is about 5 billion years old, this means that the Sun will continue to live for about another 5 billion years. At that time, because its fuel of hydrogen in its core will be used up, the Sun will begin fusing Helium… when it does that it will swell up and become a RED GIANT star; the Sun's radius will extend out almost to the location of MARS easily swallowing up the EARTH. After the RED GIANT STAGE, the Sun will stop nuclear reactions and slowly cool down and shrink to become a WHITE DWARF star.

So the Sun will never disappear totally… but in about 5 billion your years it will begin its death throes and Earth will be swallowed up.

The sun is currently in its stable "mid age", in the sense that it has "burned" (more precisely "fused" through nuclear reaction) half of its total hydrogen fuel. So it will take another 5 billion years before it runs out of hydrogen to burn. Eventually when it runs out of hydrogen, it will expand into a "red giant", in the sense that its size will be so big that it will swallow Mercury, Venus, and reach as far as the orbit of Earth. Then the sun will shrink back into a "white dwarf".

The lifespan of our sun is estimated to be around 10 billion years. Since it began burning about 4.6 billion years ago, this means that this will happen in about 4.5 - 5.5 billion years. This is due to the fact that the sun is fueled by a fusion reaction that turns hydrogen into helium. When this hydrogen runs out, the sun no longer has any fuel to keep it burning. By this time, it will have also grown to what is called a red giant star and grown bigger than the orbit of Earth.

Finally, all the outer layers of the sun will be ejected off leaving behind a small, dense star called a white dwarf, which will slowly cool down over trillions of years. The ejected outer layers are called a planetary nebula and contain elements that will eventually lead to the birth of new stars.

More detailed timeline:
universetoday

The sun will burn out in about five to six billion years, but not before becoming a red giant and frying if not vaporizing the Earth. When the sun does burn out, it will collapse to become a white dwarf - it will still be there, but be much smaller and much fainter.