I am working on a little pen plotter project and for one of my motors (which supports the pen) I have used a small DC motor obtained from an old DVD drive. I have noticed that if I supply a constant 5V to this motor, it "locks up" when the pen comes into contact with the paper and stays there whilst keeping a slight pressure on the pen (perfect for the application), but I am now starting to think, is this a bad thing? If the DC motor has a constant supply to it and is held in the same position, should it be OK? It seems to be and isn't getting hot, so I just wanted to confirm.
If you stall the motor and let it draw as much current as it wants, the motor will be dissipating more energy as heat. What happens next depends on the design of the motor.
Some motors can dissipate all of the heat when stalled. Such motor can stay stalled indefinitely.
Some motors can't dissipate all of the heat generated when it's stalled. The heat builds up, the temperature of the motor raises. That can lead to a permanent failure of the motor (possibly a fire too). For this reason, some of the motors have built-in thermal protection in the form of a bimetal strip or a fusible link.
Presumably this "constant" supply is a constant voltage. You can improve safety (to avoid possible overheat) and gentleness of the motor by limiting the current that the supply will put out. At a fixed current the motor supplies a fixed torque, which might be nice and gentle to your pen.
With DC motors you don't have the "back EMF" that you have with AC motors, so the current does not change significantly if the motor stalls. Still, as it has been suggested, you may want to limit the current to a value that holds the pen in place with the required torque, but not too much beyond that.