The neutral wire does carry current in most electrical circuits. It acts as a return path for the hot wire current to the power source. In a single-phase, 2-wire circuit, the neutral wire carries the same amount of current as the hot wire. In a three-phase setup, the current is balanced between the three wires and a neutral wire is not needed. The reason why it seems like there is no current in the neutral wire is that it is connected to ground at the service panel. This means that there is no potential difference between the neutral wire and ground, so no current flows through it.