In nonpolar covalent bonds, electrons are shared equally by both members of the bond, but they are shared unequally in polar covalent bonds. Polar covalent bonds occur when there is a difference in electronegativity, or electron affinity, between covalently bonded atoms. The polarity, or lack thereof, of a molecule greatly affects how it interacts with other molecules.
Polarity in covalent bonds is highly variable, depending on the elements involved. The only truly nonpolar covalent bonds are in molecules made of a single element, like nitrogen or oxygen gas. Otherwise, there is always a difference in electron affinity between the members of a bond, so any covalent bond between two different elements is at least slightly polar. In some cases, such as carbon and hydrogen, the difference is very slight.
Just because the covalent bonds in a molecule are polar does not mean the molecule itself is polar. For instance, oxygen has a much greater electron affinity than carbon, but carbon dioxide is not polar. This is because the oxygen atoms sit on opposite sides of the carbon, so their charges cancel each other out.
Polar covalent charges will only form up to a certain difference in electronegativity. Beyond that, instead of sharing any electrons in a covalent bond, the more electronegative member will steal them, forming an ionic bond.