Its not an easy one to answer. Like many things it depends on the mode of transport. Electricity travelling through metals will clock up a good fraction of the speed of light, depending on the metal temperature. 1/8 is a good rule of thumb thing, but at superconducting temperatures it can be much faster. Electricity travelling through electrolyte solutions can go extremely slowly. In some instances as slowly as a few meters per minute.
It can be viewed in a couple of ways.. (1) how fast do the electrons travel? (2) has fast is the *effect* of electricity?
(1) is VERY slow.. in the region of cm/minute.
(2) is VERY fast.. in the region of the speed of light.
Imagine having a row of marbles and you push them at one end.. the marbles move very slowly, but the effect of the push can be felt at the other end of the marbles immediately. Same with electrons and electricity, although incitatus is right in that it does depend on the substance you're passing electricity through.