Chagrin, yeah, I'm getting interested in trying out bare chips. Since these projects are probably going to be battery operated, I probably won't need any voltage regulator so long as I don't go above the specified voltage, right? But I will have to somehow indicate or shut off the system when the voltage has dropped below the spec. Is there a circuit to redirect the power to stop powering the chip and just flash an LED or chirp a speaker?
If your battery is of appropriate voltage then no, you don't need a regulator.
The AVR chip itself can monitor its own battery voltage. You have to set the analogReference to INTERNAL (which is 1.1V) or use an external voltage reference such as a TL341 and then measure the battery voltage against that. Once your chip recognizes that the battery is low you can set it into a sleep mode, waking it periodically to blink your LED, etc. and that will be much simpler and more efficient than any external monitoring circuit.