Rotten eggs, gas leaks, skunk spray, water contamination and hydrogen sulfide caused by human gut flora all cause the characteristic smell of sulfur. Elemental sulfur is odorless, but its compounds are not.
As eggs and other foods rich in sulfur decompose, they release hydrogen sulfide gas. This gas has other origins, including human gut flora. While the human body can absorb some hydrogen sulfide, it is released if certain types of bacteria are plentiful in the presence of sulfur-rich food being digested. Sometimes, groundwater supplies contain natural sources of hydrogen sulfide, but hydrogen sulfide in tap water is also caused by sewage contamination.
The hydrocarbons in natural gas are odorless. The sulfuric smell of piped-in natural gas comes from methyl mercaptan, a sulfur compound added to let humans know when gas leaks happen, as humans can smell one part per million of mercaptan. Mercaptan compounds are also formed by human gut flora, and they are sprayed by skunks to ward off other animals.
Elemental sulfur is also known as brimstone, which is flammable. While brimstone has no smell until it is burned, the smell caused by the resulting sulfur dioxide is strongly associated with volcanoes, which emit the same compound.