Hi,
That depends what you mean by "burn." When chemists say something is burning they mean that a substance is being combined with oxygen and producing heat. That is what is happening in a fire. Sometimes physicists describe the process of nuclear fusion that occurs in the center of the Sun as burning too, because that also produces energy.
I think what you mean, though, is whether all materials would be destroyed by the immense heat and radiation of the Sun. The answer is that any normal material you are used to on Earth would be vaporized (turned into a gas) by the Sun if it was close to the Sun for any length of time.
However, if something went through the Sun's atmosphere fast enough it could actually survive. Last December Comet Love-Joy plunged into the Sun's atmosphere and, although parts of it were vaporized, it actually came out the other side. See
http://science.nasa.gov/s.../16dec_cometlovejoy/
I should say it did not actually hit the "surface" of the Sun, but it passed pretty close. We were very impressed to see it make it out again!
Terry