supernova - When the sun explodes, will some of the planets in the Solar System survive and become rogue planets?

The short answer to your question is that the Sun's expansion will likely be insufficient to blow any planets out of orbit. It's possible that the Sun gradually losing mass could over long periods of time cause an outer planet to spiral out of orbit and become a rogue planet but that would be a gradual effect over a billion or more years, and, then, only maybe. No planets would be ejected from the rather rapid effect of the Sun expanding into a red giant.

Now, I think (I couldn't find a good link, will keep looking), but as our sun begins to burn Helium it will form a kind of stellar nebula. It won't be close to a supernova but it will cast off a fair bit of material and losing an outer planet or two during that stage might be possible - but far from a guarantee.

Would any of the 8 planets currently known, survive?

Mercury and Venus are not expected to survive the Sun going red giant but they would be eaten, not ejected. Earth is 50/50. (lots of articles on this, google "what will happen to the Earth when the sun goes red giant").

Now what happens to planets when a star goes SuperNova (which our sun won't as LocalFluff pointed out) - that's a good question. Some answers here: http://news.nationalgeographic.com/news/2011/08/110805-planets-survive-supernovas-ejected-rogues-space-science/ A supernova is likely capable of ejecting outer planets (and eating inner ones).