Which relatively simple molecules violate the octet rule? I'm learning how to draw Lewis diagrams. Everything I've read emphasizes the octet rule. However, to the best of my knowledge, that rule only applies to elements in the first three periods. 

On our exam, I expect our professor will ask us to draw some Lewis diagrams of molecules whose atoms do not comport with the octet rule. However, I haven't seen any diagrams of these; it'd be useful to get a sense of what they look like so that my gut doesn't disapprove of what will otherwise be strange looking diagrams. 

What are some relatively common molecules that comprise atoms that comprise a great number of valence electrons?
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).