Catenation occurs most readily with carbon, which forms covalent bonds with other carbon atoms to form longer chains and structures. This is the reason for the presence of the vast number of organic compounds in nature. Carbon is most well known for its properties of catenation, with organic chemistry essentially being the study of catenated carbon structures (and known as catenae). Carbon chains in biochemistry combine any of various other elements, such as hydrogen, oxygen, and biometals, onto the backbone of carbon.
However, carbon is by no means the only element capable of forming such catenae, and several other main-group elements are capable of forming an expansive range of catenae, including hydrogen, boron, silicon, phosphorus,  sulfur and halogens.
The ability of an element to catenate is primarily based on the bond energy of the element to itself, which decreases with more diffuse orbitals (those with higher azimuthal quantum number) overlapping to form the bond.  Hence, carbon, with the least diffuse valence shell p orbital is capable of forming longer p-p sigma bonded chains of atoms than heavier elements which bond via higher valence shell orbitals. Catenation ability is also influenced by a range of steric and electronic factors, including the electronegativity of the element in question, the molecular orbital n and the ability to form different kinds of covalent bonds. For carbon, the sigma overlap between adjacent atoms is sufficiently strong that perfectly stable chains can be formed. With other elements this was once thought to be extremely difficult in spite of plenty of evidence to the contrary.