OK, tell me one example, but it should be one where the force vanishes at infinity. Our world is made up of particles and it's natural to assume that fundamental forces should not depend on particles an infinite distance away. So which type of force between point objects is possible, which isn't inverse square?
I have the feeling curl F=0 is equivalent to inverse square in 3D.
Btw: Springs are objects that change shape. This doesn't count. We are talking about forces on test particles, which do not change any of the enviroment.