The Octet Rule
A Crystal Clear Chemistry Tutorial
The octet rule is as close as one can get to one of the fundamental rules in organic chemistry. It states that elements in the second row of the periodic table cannot have more than eight valence electrons around them them, whether as non-bonding electrons or in chemical bonds. Atoms can have less than eight, but they cannot have more. The classic example is that carbon cannot have more than four bonds to it.
The most common elements in organic chemistry, such as carbon, nitrogen, oxygen, boron, and chlorine, are in the second row, and this rule applies to all of these elements. The octet rule does not, however, apply to elements of the third row, such as sulfur and phosphorous.
The Noble Gas Configuration Rule
An unrelated statement that is often confused with the octet rule stated above is that elements of the second row usually want to fill up their octet (or, if it is easier, lose all of their electrons in the second energy level). This is called the noble gas configuration rule (because when the octet is filled, the electrons configuration looks like that of a noble gas), and it is more a description of how many bonds an atom is likely to want to make, rather than how many it is allowed to make. Carbon, because it has four electrons in its outer energy level, usually makes four bonds to other atoms. This way, there are eight electrons total around carbon (four from itself, and four from other atoms).
The end result of the combination of the octet rule and the noble gas configuration rule is that usually, atoms have their full octet of electrons, which means that to form a new bond to the atom, an existing bond to the atom usually has to be broken. Thus, in the example below, when the oxygen of the hydroxide ion tries to bond to the carbon of methyl bromide, another bond must be broken in order to keep the octet rule intact. Thus, the carbon-bromine bond breaks. (The electrons on bromine are not shown for the sake of simplicity.)
Another thing to realize is that usually, atoms bond to minimize their formal charges as close to zero as possible. The noble gas configuration rule says that oxygen usually has at least two bonds (so as to gain two more electrons, to go from six electrons to eight). The octet rule states that oxygen cannot have more than eight electrons around it, so any other bonds to oxygen must have oxygen donate two of its electrons in the bond (which gives oxygen a positive charge). This type of bond is called a coordinate-covalent bond. Since atoms minimize their formal charges, this means that oxygen usually has only two bonds, as any less doesn't give a noble gas configuration, and any more either violates the octet rule or gives oxygen a positive charge.
Similarly, nitrogen tends to have three bonds, and carbon tends to have four bonds. Boron tends to have three bonds, although we see that in this case, the tendency to have no charge is in conflict with the noble gas configuration rule. Thus, boron can rather easily accept two electrons from some other atom (such as oxygen) to form a fourth bond (a coordinate covalent bond). This gives boron a negative charge, but it fills boron's second energy level, giving it a noble gas configuration.
For more on bond-breaking and bond-forming with regards to the octet rule, see the article on the introduction to reaction mechanisms and arrow pushing (the octet rule appears on page 2). 