Ok, so I've been trying to wrap my head around this for quite some time, and I think I've got it. I just want to explain it here in order for an electrician to take a look at what I've got and let me know if I'm missing anything.
Conventional household wiring from the electric company has three wires; two of them carry 120VAC that are 180 degrees out of phase with each other, and the third normally has no voltage on it, with respect to ground.
The breaker panel is wired in parallel, so each branch circuit also has 120VAC available.
A 120V circuit consists of a 'hot' wire connected to one of the two 120V lines coming into the house and a 'neutral' wire that is connected to the 0V (nominal) line at the breaker.
Touching an exposed wire in a properly wired circuit creates a situation comparable to a voltage divider (potentiometer/dimmer switch/volume control). If you touch an exposed 'hot' wire, you will receive almost all of the voltage available from the power source, because the resistance in the circuit between you and the power source is considerably lower than the resistance between you and the ground.
If you touch an exposed 'neutral' wire and everything is wired correctly, you receive very little of the voltage available from the power source because most of the resistance in the circuit is between you and the power source.
However, if the neutral wire is not connected to the panel/ground, you aren't creating a voltage divider circuit, you're creating a series circuit, with your body effectively being the path to ground to close the circuit.
Do I have that right?