The trivial answer is that a carbon atom that forms 4 covalent bonds is in a lower energy state that one that forms 2. But what happens when this occurs? Carbon's valence shell is configured 2s2 2p2 (remember the p shell can contain up to 6 electrons, in a 3-D 2px, 2py, 2pz shape). Two half-filled p orbitals should mean stable molecules like CH2 - the 2 electrons from the H filling the 2px and 2py subshells. But....these don't normally exist ...instead carbon likes to form 4 covalent bonds with other atoms.
Summary
* Carbon forms covalent bonds with atoms of carbon or other elements. There is a great diversity of carbon compounds, ranging in size from just one to thousands of atoms.
* Carbon has four valence electrons, so it can achieve a full outer energy level by forming four covalent bonds. When it bonds only with hydrogen, it forms compounds called hydrocarbons.
* Carbon can form single, double, or triple covalent bonds with other carbon atoms.