Well, I was out of the regulator context, sorry.
The zener forward current x forward voltage curve is independent from the load. You can parallel a zener with a 1 ohm resistor, or a 1 Mohm resistor, the curve will be the same, so Hero's statement is very true.
A zener in series, indeed, is not to be used as a regulator, but it can be used as a voltage reference (Vsupply - Vz).
The same thing happens with a bulky design with a zener in parallel with the load, I believe, now a days, nobody uses it anymore. Why not just use them to regulate a transistorized output?