A lot depends on the sort of motor and how it's powered.
I suspect you are likely to break most servos if you try to move them away from their desired position. There is a huge gear reduction within a servo and the gears would probably break, rather than the motor burn out.
DC motors take their maximum current when they are stationary so, if you have a useful voltage to power them at speed they are likely to draw too much current and overheat if held stationary. This problem could be overcome with electronics that ensure the current stays within limits that don't cause damage. In that case it probably wouldn't do any harm to force the motor in the opposite direction. This is not a simple option, however.
Another possibility might be a stepper motor. They are designed to move in discrete steps and stay in position until the next step instruction arrives. They are unlikely to suffer damage if they are made to move by an external force that exceeds their holding force. However the computer that was controlling the motor would no longer "know" where it was.
In saying all this I am assuming you are not thinking of moving the motors at high speed or for a long time in the "wrong" direction.
...R