I have a project I want to squeeze into a small space. In order to save space, it is proving useful to 'hand craft' something like a bare bones board.
It would be useful to not use a voltage regulator, and wire the batteries (AAA's) directly to the chip. AVR's seem pretty tolerant, and anything from around 3.3v - 5v seems to be enough to get the chip to work. Plus, v. regs are a little lossy, and this shortens battery life.
Is this a dumb idea? What do I lose out by scrapping the voltage regulator?
It's not a dumb idea at all. As long as you stick with the 8 MHz versions you can operate them over the voltage range you mention.
Just remember, if you use analogRead, you'll have to make sure that the input can never go above your battery voltage. PWM may not give you the results you expect either as your battery voltage decreases.
Directly powering from batteries is an option that can work. However there is a clever device that can combine the advantage of battery power but still retain a regulated output voltage using efficent switching circuits. Adafruit has a nice product that you can study.
There's a chart in the datasheet for the ATMega that tells you what voltage you need to safely run at different clock frequencies.
Be careful with the battery voltages: remember that, even though they call them "1.5V", NiMH cells actually only charge up to somewhere in the 1.2-1.3V range.
For a really compact Arduino, consider the RBBB, the DuinoStamp, and the Mini. You may find them handier than making your own PCB. And the kit versions can be built to run off 3.3V (the flavor of the Mini I linked to is already built for it).
@retrolefty: Yep - I'm familiar with the mintyboost. Maxim make a very nice boost converter chip (MAX619, I think) that basically does everything the mintyboost does, but in one chip (cheaper too). I am severely constrained for space, so don't want to use anything more than I absolutely have to. Still, that is certainly something to consider.