Can an Arduino power itself off [not low power mode] via software? I'm working on a sketch where an Arduino UNO performs no useful work after the first 10 minutes following power on.  It is not needed again until power to it is shut down, then re-enabled.  This may not happen for hours or even days.  No wake-up function is required, or deemed useful.  

Of course, the Arduino could simply be left on as long as it's connected to its power source, but it will be placed remotely, and it seems [to me] safer to have it powered off. when not in use.

In essence, the Arduino is powered by a wall wart and plugged in with other devices fed by a switchable 120v power source.

I found a couple of possible hardware/software solutions to the problem but it isn't clear whether they would work in this situation.  Power consumption is not the issue here.
In general, an Arduino by itself has no control over its power input.  It can, of course, enter various Sleep modes, such as the Power-down mode with watch-dog-timer off, which uses 0.1  μA.

It isn't clear from the question what will turn the Arduino back on after it is off for a while, but if you have either a push-button or a signal to turn it back on, the Pololu 2808 Mini Pushbutton Power Switch will work as an Arduino-controlled off switch.  This board has On, Off, Ctrl, and button-contacts inputs.  If your Arduino raises the Off input, power shuts off cleanly.  To turn it back on, either connect the  button-contacts inputs together, or raise the On input, or pulse the Ctrl input.