MightyOhm.com

Because the recommended family of USB serial adapters have a 5 volt supply lead it is really trivial to use a 1904 regulator to provide power. I just wire wrapped the ground pin of the 1904 to pin 3 of the pulse header, the output pin to pin 1 and connected the input pin to pin 3 of the serial header. I used the case screw adjacent to the pulse header to hold the regulator chip, the power draw of the geiger counter isn't sufficient to need an additional heat sink. I left the batteries out, but leaving the power switch off would isolate them. Since pin 3 of the serial header is not connected to the counter board a 5 volt, 12 volt or even somewhat higher DC source can be hooked to pin3 and grounded to pin 2 of the serial header if you aren't using a USB adapter.

Nicely done!

Is this the regulator you are using?
http://www.nteinc.com/specs/1900to1999/pdf/nte1904.pdf

Yes it is. It has been plugged into my Raspberry Pi for a week now logging useless background count data.

This is great! I'm thinking of adding a fuse to the +5V rail from the serial header when doing this, just for good measure. Any idea what the maximum current draw is?

No idea on current. I evaluated the heat sink question by letting it run for a while and feeling the tab.