The electrons in a conductor will move approximately near the Fermi velocity I believe. For copper, this is less than 1% of the speed of light. This speed is not constant, either, and is subject to statistical considerations (some move slower). One thing to note is that while the electrons move at tremendous speeds, they are not all moving in the same direction. The overall velocity, called the drift velocity, is on the order of millimeters per second. This is analogous to how, even on a calm down, air molecules are themselves moving around at hundreds of meters per second despite having little or no overall velocity.