All 16 Boolean Logic Gates
What do you mean by real? You can define as many logic gates as you want and build them. However, in a boolean logic with 2 inputs, there are 16 different combination of outputs. On the other hand, it proven that $\{AND,NOT\}$, $\{OR,NOT\}$, $\{NAND\}$ and $\{NOR\}$ are functionally complete (which means we can build all other combination from 16 outputs with only using gates in those sets ). 

However, you may build a new gate directly with a technology (let say MOSFET) and use another name. You can still build that gates using one of the comprehensive gate set.