Which relatively simple molecules violate the octet rule?
There are 3 types of octet rule "violations" or exceptions


molecules with an odd number of electrons, such as nitric oxide




(image source)


molecules with less than 8 electrons around an atom, $\ce{BeCl2}$ and $\ce{BH3}$ serve as examples




(image source)


molecules with more than 8 electrons around an atom, such as $\ce{PCl5}$ or $\ce{SF6}$




Take a look at the image source links for other examples as well as some practice problems.  

The bonding around electron deficient atoms such as the boron in $\ce{BH3}$ is best explained in terms of 3-center 2-electron bonds (reference; SE Chem example_1, SE Chem example_2)).

Sometimes, arguments based on d-orbital involvement are advanced to explain the bonding in atoms surrounded by more than 8 electrons.  However d-orbital involvement in non-transition metals is now generally considered to be unlikely.  Instead hypercoordinated (or hypervalent) bonding in which 3-center 4-electron bonds are formed has become a more generally accepted explanation.  A number of examples have previously been discussed here on SE Chem (for example, see here).