All organic compounds contain carbon. Carbon is so important to the structure of organic molecules that organic chemistry has been called the study of carbon and its compounds. Other elements are readily incorporated into organic molecules, though the determining feature of an organic molecule is the presence or absence of carbon atoms.
Carbon is unusually eager to form bonds with other atoms, which makes it ideal for building up the large molecules used by living things. To build these molecules, carbon commonly bonds with hydrogen, nitrogen and oxygen. Organic molecules are sometimes able to incorporate other elements as integral parts of their working structure. An example of this is in hemoglobin, which is a type of organic molecule called a protein. Specifically, hemoglobin is a metalloprotein, which means it incorporates atoms of iron into its active site to better capture and transport oxygen in red blood cells.
While all organic compounds are built around carbon, not all carbon-based compounds are regarded as organic. For reasons that have more to do with the history of chemistry than with the intrinsic properties of the molecules themselves, carbon monoxide, carbon dioxide and tungsten carbide are not classed as organic even though they contain carbon bonded with other elements.