Covalent compounds include methane, carbon dioxide and water. A covalent bond is formed when electrons are shared between compounds, and electron pairs are created as a result.
Water is a covalently bonded compound because the two electrons from the two hydrogen atoms are shared with two electrons from the single oxygen atom. Each hydrogen effectively "sees" two electrons, which fill its outer shell.
Similarly, the carbon in methane shares a single electron with each of the hydrogens around it, filling its outer shell for stability. Again, the hydrogen experiences the effect of two electrons, contributing to its stability. The covalent bond is not as strong as the bonding in water or carbon dioxide, which is why methane decomposes into these two molecules when it burns.
Covalent bonding can occur in compounds that are traditionally considered ionic. MgSO4 is magnesium sulfate, and while the bond between the magnesium cation and the sulfate anion is ionic, the bonds between the sulfur and oxygen are strictly covalent, as they share electrons with each other.
Xenon, one of the noble gases, can also exhibit covalent bonding under moderately extreme circumstances. It reacts with fluorine to create xenon difluoride. In this case, the two fluorine atoms share a single electron with the xenon.