I have some 12 V motors, and the corresponding motors controlers like these here http://imgur.com/XBEww. Every other 12 V power supply I have seen is either very expensive or has extremely low amps, where even a $20 computer power supply will provide like 10 amps at 12 volts. Is it possible to use a computer power supply to control some 12 V motors with my Arduino and these motor controlers?
Yes, you can use a PC power supply as a general 12V supply, but there may be some extra requirements.
Some early PC supplies required a substantial minimum load on the 5V output to stabilise the supply. I believe this is less common now. If it was a requirement you could "waste" some 5V output energy by connecting a light bulb or resistor or other suitable load.
PC power supplies may often have coupled output inductors to increase switching noise filtering capability. Noise level and voltage accuracy may suffer using 12V only, but with motors as a load this should not be a major issue.
So - yes, it will probably work OK. Trying it is easy enough. You don't need a motor controller to start - just connect the motor to the 12V output wide open throttle mode ...). If the 12v supply does not sag appreciably you can probably make it work.
You need to know about PC power supply starting link, power good, ... bu this is all well covered on the internet.
A computer power supply does power motors: those in disk drives and fans.
It's a matter of matching the peak current delivery ability of the power supply to the peak current demands of the motors (inrush current), as well as under steady state conditions.