What is Markovnikov's rule?
Markovnikov's rule is used to predict how (for example) HX, where X is a halide, adds to an unsymmetrical olefin.  As the diagram below shows, Markovnikov addition follows the rule that the "H" will add to the least substituted carbon while the "X" will add to the most substituted carbon.  This is due to the fact that these reactions proceed by protonaton of the olefin to yield a carbocation.  Protonation at the least substituted carbon yields the most stable carbocation (in this case a secondary carbocation).  Finally the carbocation reacts with $\ce{X^-}$ to yield the final product.



In some cases the Markovnikov rule is not followed.  Such additions to olefins are termed "anti-Markovnikov".  These reactions typically proceed through a radical intermediate rather than a carbocation.  For example, addition to the olefin might be initiated by the addition of a bromine radical to generate the most stable radical intermediate, which would place the radical center at the most highly substituted carbon. Addition of a hydrogen radical completes the process and generates the final product which has the reverse addition pattern as compared to the Markovnikov addition product.