The blackbody does not exist. Indeed, every body reflects radiation to some degree, while by definition the blackbody should absorb all the radiation it receives, independently of the body's temperature and the composition of the radiation spectrum. Why then do we use this notion, at first place? The reason is that its radiation intensity and spectrum decomposition only depend of the blackbody's temperature and thus can be theoretically computed. This accounts for the special significance of this notion in radiation theory.
The best approximation of a blackbody may be a rather big niche with a small hole and inside walls with uniform temperature which reflect and partially absorb radiation. The rays reaching the hole are reflected several times within the niche and are almost fully absorbed. If the inside walls of the niche have high temperature (like that of a hot stove), the parameters of the radiation leaving the hole are quite similar to those of blackbody radiation. In particular, they do not depend on the material the niche is made of.
However, there is a radiation in nature that resembles blackbody radiation very much. The measurements performed in the last few years by the COBE satellite have proved that the so-called relict radiation, an electromagnetic radiation filling the entire universe which is not produced by stars, galaxies nor dispersed matter, agrees with the radiation of a blackbody at the temperature of 2.73 K up to a factor of the order of 1/10,000. This radiation is a relic of the Big Bang. Fortunately, the differences in the spectra of the relict radiation and of the blackbody radiation at the level of 1/10,000 play a significant role in the Big Bang theory: they are used to explain the origin of galaxies and stars.