Data logging options that require no power supply

Hi,

I am looking at my options for logging data on an Arduino mega 2640.
I think I can use a sheild:

Where I would just keep a flash drive plugged into the shield while data is being collected,

Or a dataflash chip:
http://playground.arduino.cc/Code/Dataflash

The problem is that I am already using both the 3.3 and 5 V power supply for a GPS chip and an MCU. Is there any way to log data that doesn't require a power supply? Or is it possible for me to use those power supply ports to power two components simultaneously?

I am very new to Arduino and electronics in general, so I apologize if I'm in way off-base. Any direction would be greatly appreciated.

Farm the data logging out to an external logger.
http://forum.arduino.cc/index.php?topic=252905.0

The whole concept of Arduinos is that you can stack shields which derive power from a common supply. Needless to say, there is a possibility that the combined stack will demand more power than the 2640 can supply. Adding a sensor shield is not likely to cause this. A GPS shield might, in which event it probably has its its own power jack