Alan, consider 2 possibilities:
1.) 2, 20A single pole breakers are in adjacent slots 1 & 3 in in a 120/240 single phase panel. Each circuit has its own neutral conductor landed on the neutral bus bar. The circuits supply your living room. (You just moved here.) You happen to have your TV as the only load on one circuit and an 1800W space heater as the only load on the other. If one of those neutral conductors should come loose, you will either be watching your TV in the cold or reading a book in the warmth. You probably won't be letting the smoke out of anything.
2.) Since the two circuits above are on opposite legs, a common neutral is permitted. One white wire is landed on the neutral bus and it is carrying the difference current between your two loads. Today, it happens to be the return current from your space heater. Things get really interesting when that neutral comes loose. Basically, you're left reading a book in the cold wondering what you're doing in USA. Meanwhile, Your TV is climbing through 500 feet thinking it has just been plugged into an outlet in the North of France. The voltage to the TV would have increased as the heating element was cooling, dropping almost all of the available 240 Volts across the TV mains.
We always run the risk of an unequal split from a failed center-tap connection from a transformer. Shared neutrals, while working fine most of the time, do offer the potential for more exciting failures. Even with a proper panel Neutral, loads on breaker pairs with shared neutrals are at a higher risk of over voltage.
Consider a case where the shared neutral is intact but the space heater suffers a direct short. It would not be unreasonable to have half the voltage drop on the hot and half on the neutral until the breaker tripped. This could add 60 volts to the other leg's 120 for a short period of time. (But it doesn't take long to let the smoke out)
Joe
[This message has been edited by JoeTestingEngr (edited 01-06-2007).]
