How fast do electrons travel?

In wires and other conductors, electrons travel very slowly. They drift along at molasses speeds, like 1 mm/sec.

In vacuum tubes, electrons travel more quickly, around 1% of the speed of light.

But the speed of the electrons isn't really important for circuits. What matters is the speed of electric field waves. These waves travel down the wire almost up to the speed of light, and they are responsible for the "instantaneous" effects we see from electricity.

Think of a wave traveling across the surface of a slow-moving river, or the speed at which sound waves travel through slow-moving air. Waves can travel much faster than the medium that carries them.