Electricity travels at nearly the speed of light.
Electrons themselves travel like molasses:
"In the case of a 12 gauge copper wire carrying 10 amperes of current (typical of home wiring), the individual electrons only move about 0.02 cm per sec or 1.2 inches per minute (in science this is called the drift velocity of the electrons.). If this is the situation in nature, why do the lights come on so quickly [when you flip the switch]? At this speed it would take the electrons hours to get to the lights."
This completely caught me by surprise, but it makes sense once it's pointed out. Imagine a pipe filled with solid balls that just fit in it, with little friction. If you push a ball in one end, a ball pops out the other almost immediately. But not the same ball! Even if you keep pushing balls in, that first one you pushed will take a while to get the other end.
Update: as rrobukef notes in a reply, this would be the case for direct current (DC). With the usual household alternating current (AC), the electrons barely move at all!
https://www.uu.edu/dept/physics/scienceguys/2001Nov.cfm
https://wtamu.edu/~cbaird/sq/2014/02/19/what-is-the-speed-of...