How fast does electricity travel?

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First you have to understand what electricity is and if it travels. If we are talking about an electric current, the current is the movement of charges (real or their mathematical abstraction) in a medium. In the vacuum these charges are represented by electrons and other charged particles (protons, positrons, etc.) which also have mass and, therefore, can not reach the speed of light.

Within conductors, the real (electron) or virtual (the mathematical negative of the electron) charges are limited by the resistance of the material which is always greater than the resistance that that material opposes to the light.

But in electricity we do not usually import the velocity of charges, but their flow. Actually what we understand as current is the flow (quantity of charges passing through a point at a given moment). We could then understand the velocity of electricity as the velocity after which the flow is the same across the entire length of the circuit. The speed it takes a wire when I put an ampere on one end and measure an ampere on the other. The cable not only opposes the speed of the loads but also the relatively static loads, must move. The response of the medium to this motion is called inductance and is a limiting factor that depends on the rate of propagation of the information in the medium.

But we could understand electricity, not as currents in a circuit, but as electromagnetic propagation. If I have a load oscillating in a vacuum, what is its velocity? And the answer is the speed of light because the propagation of that information is light.

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Video credits:   RimstarOrg