Most people have heard the common theory of how our planet is going to die. Class G stars, like our sun, live for billions of years, combining hydrogen atoms into helium atoms to create energy. The process is known as nuclear fusion. When the star runs out of helium, however, the core shrinks due to gravity, and the star cools and begins to expand, turning red and becoming what's known as a "red giant". At this point in time (which is billions of years from now), it's likely our sun will have engulfed Mercury and Venus, and possibly Earth. Millions of years after this, the sun will shoot its outer layers into space, which will then destroy the Earth, if it hasn't already been destroyed, and Mars. It's unknown whether this will affect Jupiter and the other gas giants, though it will disrupt their orbit. After this, the sun will become a white dwarf, and dim, hot star that shines for billions of years until it darkens and becomes a black dwarf. By then, however, our planet will have been destroyed.
Other planets orbit stars similar to our own, or ones hotter or cooler. When these stars die, they will essentially kill the planets in a similar way. For planets orbiting a neutron star, a neutrons tar collapses and turns in to a black hole when it dies, which could engulf all of the planets in the solar system or completely change their orbits. For planets orbiting a binary star system, the binary star could collapse and destroy many planets, or one could explode and blow up the other, and the remains could form other planets and create new ones. So, even the death of planets can result in new planets.