There would be catastrophic consequences. The Earth is spinning on its axis at 368m/s due East and we are spinning with it. If the Earth were to suddenly stop, then all matter on the surface of the Earth that doesn't directly make up the Earth would continue to be moving as it was.

This would cause buildings, trees, animals and us humans to fly due East at over 1,000 miles per hour-the speed of a bullet fired from a rifle. There wouldn't be much left of human civilisation if Earth were to suddenly stop moving.