What is the noble gas configuration of copper?
$\ce{[Ar] 4s^1 3d^10}$  is the correct configuration for copper. Why?   

In simplest terms, some elements do not follow the Aufbau principle, so there are some alternate ways that electrons can arrange themselves that give these elements better stability.

Copper is a transition element and transition elements like either half filled orbitals or fully-filled orbitals. This makes them more stable.

For example:

Using the Aufbau principle, you would write the following electron configurations:


$\ce{Cr = [Ar] 4s^2 3d^4}$
$\ce{Cu = [Ar] 4s^2 3d^9}$


However, the actual electron configurations are:


$\ce{Cr = [Ar] 4s^1 3d^5}$
$\ce{Cu = [Ar] 4s^1 3d^10}$