What real-world examples show not work being done? Can you think of examples other than resisting the force of gravity?

Work is defined as a force doing a movement, for example, if with a force F we move an object a distance D, the work done is:

W = F*D

(note, the force is causing the movement, the product here is a dot product, this means that if the force and the displacement are perpendiculars, the product is zero)

So the examples where there are not work being done may be:

We do not have any movement:

For example, you can go to a wall in your house and push it really hard.

There is a force, but the wall will not move, so we have D = 0

and W = F*D = F*0 = 0

Because we have no motion.

Another case is where the force and the direction of motion are perpendiculars.

If we have for example a car, moving at a constant speed, and you push it sidewise (perpendicular to the direction of movement) we have a force being applied and movement, but those are in different directions (so the force does not cause the movement) so we dont have work being done.