I've never tried working with something that requires more power then my board, the Arduino in this case, can output. For my recent project though I'm thinking of using 3 of these babies:
My question is, how do I power these things? I was going to use 3 74HC595's to drive them but obviously those don't put out enough juice.
Thanks,
BlackNoir
Just use transistors .
Connect output pin to Transistor which makes it possible to switch a higher current.
Could you recommend one? I'm not sure what I need to look at to figure out which to get.
The maximum forward current is 25mA, almost all small signal transistors can do that.
If you plan to pulse the segments the maximum pulse current is 150mA.
Then you need to look at the maximum collector current of the device.
Then you calculate the voltage drop over the device. This will give you the power loss, and that can you find in the data sheet again.
If the driver transistors get to hot you might need a heat sink.
But all these devices are quite cheap, the worst thing that can happen is that the transitors get too hot, and maybe brake.
But analyse the failure and you will know how to do.
You might also try mosfets. 2N7000 ought to work, they are cheap and should not put out as much heat. Whether you use these or ordinary junction transistors, remember to add a current limiting resistor in series with each display segment and its driver transistor or mosfet or something will burn out! 
Since the LED's are Common Cathode, can I run my 9v source through either a transistor or a mosfet? All the examples I've found have the ground going through them.
Thanks for all the replies btw.. can't wait to give this a try... i'll probably just pick up both types and see which one works best for my setup.
You could use with a Darlington array. I recently bought one myself (haven't used it yet): they're small (16 pin DIP), cheap and they can handle high currents and high voltages.
I'm thinking I'm not quite at the level of knowledge yet to handle the Darlington Transistor Array.. looks good though.. I'd probably just burn it out though.
It would probably easier to handle the darlington array than individual transistors. if you get an array with 8 pairs they would match up nicely with the 595 shiftregisters.
EDIT:
If you use an eight darlington array like ULN2803, it's a matter of hookin up each output from the shiftregister to an input on the ULN2803, and then drive each segment of the 7 segment LED's with an output from the ULN2803.
Blacknoir: I forgot about these darlington chips when I suggested mosfets. Don't let the internal circuitry spook you! Just treat it as 8 transistors in one box. On the pins, B=base, C= collector. Same number= same transistor. All the emitters are already tied together for you; you only have to connect that one pin to ground.
All the replies so far seem valid to me. The choice is yours. My advice is to build just the circuitry for ONE display first. As I said before, put in resistors to limit the current. If you don't know how to work out the value, just ask. Unlikely anything will blow then, but if it does, you figure out why and that's one more thing you know 
Thanks for the help everyone. I'll order the parts and give it a try.