Can I use the 12V line of a computer PSU to power my circuits?
Yes. 

There's not much more to say than that ;) 

Getting them to turn on though can be a bit tricky. Some may require a load on the 5V before they will allow you to turn them on (a simple resistor will do), some may require the load on the 12V (in which case you're fine), and some don't care either way. 

To switch a normal ATX power supply on you need to connect the green wire to ground.  I often use an NPN transistor to act as an MCU controlled switch to control the power.

I have a small one embedded in my desk powering all sorts of things - PIC32s, audio amplifiers, a bunch of binding posts for powering whatever I'm working on...  It's a really handy power source, The -12V is also great to have available.