You might want to note that the speed of the current is not the same as the speed of the electrons. The drift velocity of the electrons mentioned by Ben Niehoff is *snails pace*. It would take something like a year or so for a single electron to cover the distance from the plug to the household applicant, assuming it runs on DC. In an AC circuit the average drift velocity of the electrons are zero.
But the electric field that drives the electrons propagates through the wire at near speed of light, so *all* conduction electrons in the wire begins to move at nearly the same instant, and thus the speed of the current would be the speed of light in the appropriate medium.
Hope this helps.