I've seen discussions of using an old 240V wire (two hots, a neutral, and a ground) and reconfiguring it to have two 120V circuits.
As an example, if it is a 20A cable, you could have two 20A circuits, each one using one of the two phases and both sharing the neutral and ground.
If each circuit is powering a device using the full 20A, would this result in 40A of current going onto the neutral, causing overheating?
Additionally, will sharing the neutral cause interference between the circuits?
Actually, it would result in a net 0 A on the neutral. So this actually can work quite well and is called a Multiwire Branch Circuit or MWBC.
The one catch is that the breakers powering the circuit need to be set up for common shutoff - i.e., if you turn off one, you always turn off the other. If the breakers are actually set up for common trip, which is normally the case for a 240V circuit like a stove or dryer, then that provides common shutoff as well.
Just to expand the explanation in the answer from @manassehkatz:
On a USA-type 240 volt circuit, you actually have two 120 volt hots, as you know, but the AC signal is 180 degrees out of phase. So when one hot is at +170 volts (peak voltage for 120 volts RMS), the other hot is at -170 volts and when one hot is at 0 volts, the other hot is also at zero.
The result is that on a 20 amp circuit, the most current that can travel over the neutral is 20 amps and this occurs when the load is completely unbalanced: 20 amps on one hot and 0 amps on the other. In this case, all of the current from the load returns over the neutral.
On the other extreme, if both hots have a 20 amp load, then all of the current from one leg returns over the other (effectively, the two loads are in series) and no current has to travel over the neutral.
