The two properties of carbon that lead to the huge number of carbon compounds we see around us are:

1. Catenation: Carbon can form very long chains of interconnecting carbon-carbon bonds, which is a property called catenation. Carbon-carbon bonds are strong and stable, and through catenation, carbon forms a countless number of compounds. A tally of unique compounds shows that more contain carbon than do not.

2. Tetravalency: In most stable compounds of carbon, carbon obeys the octet rule and is tetravalent, meaning that a carbon atom forms a total of four covalent bonds (which may include double and triple bonds) . This allows carbon to bond with a wide variety of other elements, including hydrogen, oxygen, nitrogen, and sulfur, forming a vast array of organic compounds.

These two properties of carbon, catenation and tetravalency, allow carbon to form a seemingly endless variety of compounds, including those found in living organisms, fuels, plastics, and many other materials.