Do you mean motion or acceleration? Say you drop a ball from a great height, when it reaches terminal velocity the drag load due to air resistance upwards will equal the weight of the ball acting downwards, in which case the sum of all the forces acting on the ball is zero and it travels at a constant speed. So in this sense there is "motion with no force". If you want to change the speed however then you need to accelerate the object and to do so you need to apply a force (F=MA).
I'm thinking of a constant-velocity force. Is this an example of a constant-velocity force ie. without acceleration?
Under constant velocity there is either no force, or the forces (which are all vectors ie they have direction) cancel each other out. In the example the force upwards (air resistance) is cancelled out by the force (weight) downwards.
Newton's 2nd law of motion says that the net force on an object is its mass times its acceleration. Therefore, any object that is not accelerating has no net force on it. That doesn't necessarily mean it has no forces acting on it - just that the vector sum of all the forces acting on it adds to zero. Newton's 1st law says any object that is not accelerating will keep moving at constant velocity (which may be zero) in a straight line.
