Carbon forms covalent bonds due to tetravalency i.e., have 4 electrons in the outer most shell. Losing and gaining 4 electrons is not possible due to effective nuclear charge, thus electrons are shared to form covalent bond.
Two reasons for large number of carbon compounds :
(i) Catenation : Ability of a carbon atom to form bonds with itself giving rise to long chains.
(ii) Tetravalency : Since carbon has a valency of 4 , it is capable of bonding with four other atoms of carbon or atoms of element like oxygen, hydrogen, nitrogen, sulphur, chlorine etc.
Carbon forms strong bond with other elements because it is small in size due to which nucleus holds shared pair of electrons strongly.