oric_dan:
If I want a 3.3V supply from say a 9V battery is there any disadvantage in using the output of a 5V regulator as the input of a 3.3V regulator rather than wiring the battery straight to the 3.3V ?
First off, as always come up around here, the little 9V batteries don't have enough energy
to run an Arduino for very long.
True. However, the OP is probably talking about a standalone atmega328 or similar arrangement, otherwise he wouldn't need voltage regulators. A 9V battery can power an atmega328p for quite a long time, if you don't have a USB-to-serial converter taking additional current, and you reduce the clock frequency to 8MHz or lower. What you shouldn't do is run motors, solenoids or other high current devices from a 9V battery.