Arduino power supply

Hello,

I am using two arduino boards for my project. The first board is powered by a 9V DC power supply. To power the other board, I have the 5V output from the first one running to the 5V pin on the second one. I read online that powering the arduino this way is not recommended because it won't be regulated. However, since I am using one arduino to power the other, it will work, right? It will be regulated so I don't see any issues... Anyone see any problems with doing this?

Connect Gnd too.
On the 2nd board, add a diode from 5V (anode) to Vin (cathode) so the regulator is not reverse driven too much. Other than that you're fine.

However, since I am using one arduino to power the other, it will work, right? It will be regulated so I don't see any issues...

Right. The 5V out of the Arduino is regulated. You are pulling twice the current from the regulator (assuming the two circuits are similar), but if you are not powering a bunch of stuff from the same supply, you'll probably be OK.

I'd be inclined to "spread the load" and supply 9V to both boards (if that's convenient). Power consumption will be the same either way, but the heat dissipated by the regulator(s) will be divided instead of all the heat coming from one regulator. If you are powering additional shields, of if you ever use a higher-voltage supply (with more voltage dropped across the regulator), then, I'd split the load between the regulators.

The regulator on one board carries the load for two. The 7805 regulator wastes everything over 5V given to it directly into heat. Run your setup and see how hot the regulator gets, it's probably okay.

Keep on the lookout for dc-dc buck converters. Feed your 9V or 12V to one of those and the extra voltage gets converted to amperage and only a little heat. Take care not to end up past the max amps. My cheap ones are good only to 3A output, voltage is by adjusting screw. They cost less than $2 each.

Easier and cheaper would be to get a 5V 1A regulated switching-power wall wart and hack the cable, split it in two, common power and grounds, maybe put a bypass cap or protection diodes in there?

It's not a 7805, its a NCP1117. Still a heat dissipator tho.
Y-cable (splitter cable) from 7.5V or 9V source to both barrel connectors would be good.

CrossRoads:
On the 2nd board, add a diode from 5V (anode) to Vin (cathode) so the regulator is not reverse driven too much.

Keep in mind there will be a voltage drop on the diode (0.3V to 0.7). The board will work, but if you'll be using the ADC of the second Arduino your Voltage Reference will be wrong.