Michael, there are few points to consider.

1) When you switch power off to *some* components of a bigger circuit,
and in this case the PIC board AND the PC hardware makes a big circuit,
you have the risk to current backflow. It means that when your PIC
circuit is powered off, and the PC still powered on, some PC's RS232
lines would be carrying voltage, enough to backflow into your PIC or
RS232 chip on the PIC board, via their I/O pins. This current will end
up at the PIC +Vcc and *can* cause problems, as keep the PIC "half"
powered on, or something like that.
In other words, your PIC board will be receiving voltage at some I/O
pins, while its VCC is off.

2) Two control power to the PIC board is quite simple, even that you
already said about power consume, really small, feeding by a 9V
battery.  A simple BS170 small FET transistor controlled by one PC's
serial lines it is enough.

                                     .-------(+)9VBattery(-)--Gnd 
                                     |
                          BS170      |
                  20k           ||---'
PC RTS-------------R------o-----||-->.
Swings                    |     ||---|
Below -8V                 |          |
Above +8V                ---         o-------> PIC + 8.x V
                1N4148    A          |
                          |         --- 100µF
                          |         ---
                          |          |
                         Gnd        Gnd 


3) If your circuit is really small, and consume low power, you *should*
consider feed power to this little board directly from PC's Rs232 lines,
so you really don't need to worry about a 9V battery power savings.

4) As the communications between your PIC board and the PC would use
just few lines, as RX, TX, Gnd and probably a Power Control, and also
considering that your PIC circuit is a A/D conversion thing, that would
be measuring external elements, I would suggest to install a tripple. By
this way, your PIC board would be really and completely isolated from
the PC's serial voltages. The first optocoupler would be used as
PIC_TX_to_PC, other as PC_RX_from_PC, the third one as PC_Power_to_PIC. 
Actually there are low power opto-couplers, and obviously in this case
you would still using the 9V battery. 

Wagner.

"R. Michael O'Bannon" wrote:
> 
> I've just designed a plain vanilla 12-bit A/D conversion board using a
> 16F84A.  The PIC controls the A/D conversion speed and sends data to the
> serial port of a PC at 9600 baud.  On the PC side, QBasic reads the serial
> port and deals with the data.  The board is powered by its own 9-volt
> battery.  To complete the design, I would like to be able to turn the power
> to the board on and off using one of the serial control lines.  Since it is
> battery powered, the circuit needs to present a minimal drain to the battery
> when the board is off.  Could someone suggest an easy circuit for doing
> this?  Low parts count would be nice.
> 
> Thanks in advance.
> 
> Michael O'Bannon, Ph.D.
> Atlanta, Georgia