Find the right motor to lift a robot's arm
Note that I am an EE, not a mech engineer, so take everything I say with a grain of salt.

Torque is a mass times a distance. Motors are typically rated in oz-in, or kg/cm. If I have a motor rated for 16 kg/cm, this means that I can have a 1kg load at the end of a 16cm massless rod. Obviously there are no massless rods (thanks for nothing, Higgs Boson). If we take the distance from thr center of mass with load attached to the "gripper" or whatever to where the motor is placed, and multiply that by the mass of the whole thang, you should get the rating of motor that you need. 

Now that you have that, you need to figure out what type of motor you need. A typical spur gear motor has low accuracy, but relatively high torque for the size. It's also really easy to drive these. The robotic arms I've had have all had spur gearmotors. The one shown has 16.7 kg/cm of torque.

A stepper motor (say, this one) is really, mind-bogglingly accurate. They're also pretty torquey. However, they'll be a bit harder to drive.