Yes, one of the number one questions people have about the Sun!
We do expect the Sun to burn out, but not for a very long time. We expect it to slowly heat up and in about 5 billion (5,000,000,000) years it will run out of the hydrogen in its core. This is the material that fuels the Sun. In the Sun's core immense pressures convert hydrogen into helium and energy in what is called nuclear fusion.
Once the Sun runs out of hydrogen we expect it to start burning the helium that has built up in the core. Then it will expand into a red giant star - cooler, but much larger. It may even expand out to the Earth's orbit. That seems to be a bit strange that it will get bigger before it burns out, but that is what we expect.
Eventually the red-giant Sun will loose its outer layers leaving a bright, small (about the size of Earth) white dwarf star, which will cool over billions of more years.
Other stars that are larger than the Sun explode in supernovas, but we don't expect the Sun to do that.
There is more about the lives of stars here:
http://www.windows2univer...ff/tourstars_1a.htmlhttp://www.pbs.org/seeing.../lives-of-stars.htmlTerry