When do we know to change from cartesian to cylindrical or spherical coordinates?

We may solve a function or check a theorem but sometimes the mathematics is easier when we switch from different coordinate systems. What can we look for that tells us changing is a good idea?

For example we expect an electric field of a point charge te be equal in magnitude at equal distances from the charge. The coordinate system that works in the same way is the spherical system. There the distance from the origin is simply r, while in a cartesian system it's $$\sqrt{x^2+y^2+z^2}$$