I'm about to order some 24V Steppers. I have a spare computer power supply. I noticed that on the pinout, theres a +12V and a -12V. Can this be used to supply the 24V?
Inquiring minds want to know. Cheap minds too 
No it can not.
What PC PSU do you have that has a -12V rail? Much older ATX PSUs use to have a -5V rail but that has long since been done away with.
The question is can you connect a pair of ATX PSUs together in series to give you the 24V you need? Not sure if a switching PSU is able to do that.
I was looking at a PC power supply today that had a -12 VDC rail; granted it could only supply about 500 mA, so it probably wouldn't work well for a stepper driver, but it did have such a rail!
As far as connecting two power supplies in series? My gut instinct says that's a bad idea...
If you need 24VDC to run stepper motors, your best bet is to look into telecom power supplies; sometimes you can find wall warts of this nature that are used for switches and CSU/DSU boxes meant to be installed in a telco. I have seen such power supplies cheap at thrift stores, too. However, wall warts might not have the current pushing ability you would need to say, run 3 steppers all at the same time (like for CNC).
At that point, your only option is to buy a power supply with the current handling capability you need; don't cheap out and try some hack job, it will probably only lead to grief.
Finally - are you sure the steppers won't run on 12VDC? Sometimes you can get away with it (albeit with less torque, of course).
My PSU is an ASTEC model ATX200-3505. The 20-pin connecter has a blue wire that's supposed to be -12V. I haven't actually measured it, so I can't say it really is. ATX power supply connector pinout diagram @ pinoutguide.com
The sticker on the side of the PSU says I can get 800mA at -12V. It also has a -5V rail, max 500mA. The +12V rail is max 6A, so I should be ok there.
I imagine I can run the steppers at 12V, but I also imagine I won't get the stepper's full torque at that level. I'll try it and see if I get enough.
You can get Universal lap top PSUs from Ebay that are cheap and are adjustable up to 24V 
No it can not.
Yes it can.
I can get 800mA at -12V. It also has a -5V rail, max 500mA. The +12V rail is max 6A, so I should be ok there.
So that means you will be OK getting 800mA at 24V - that's all. You then have to have the arduino ground connected to the -12V line, and make sure there is no connection between the arduino's ground and this power supplies ground which will then be floating at 12V above the arduino's ground.
Remember when you connect a USB lead you are using the PS's ground so this has to be septate from your PSU's ground, that might mean removing the mains ground lead from the external PSU. Some people might baulk at that.
I'm glad you pointed this out. I would not have guessed to put the Arduino ground to the -12V.
I have a 3-prong to 2-prong plug. So I'll use that for this experiment.
Thanks for the heads-up