How fast do electrons travel when moving as an electrical current through copper wire?

The actual velocity of electrons through a conductor is measured as an average speed called drift velocity. This is because individual electrons do not traverse straight line paths in conductors, instead they move in a random zig-zag motion, changing directions as they collide with atoms in the conductor. Thus, the actual speed of the electrons through the conductor is very small in the direction of current.

For example, the drift speed through a copper wire of cross-sectional area 3.00 x 10^-6 m², with a current of 10 A will be approximately 2.5 x 10^-4 m/s or about a quarter of a milimeter per second.

What is Plasma?

A plasma (or, more properly, an electromagnetic plasma) is a phase of matter that has enough energy for the electrons to separated from the nucleus. It consists of independently moving electrons and nuclei, and thus has some rather interesting properties, such as very good magnetic shielding. It can be found in places such as the center of the sun, and also, in small quantities, surrounding a lightening bolt. 

Many people consider solid, liquid, gas and plasma to be the only four phases of matter. This is not true, as there exist many others, but they are generally more exotic with names like hadron gas or Bose-Einstein Condensate.