Whether as a metaphor, or in real life, the day the Earth stops spinning is certainly a day to dread. For starters, at the Earth's equator forms a bulge, due to centrifugal force. This helps to keep the world's oceans in their respective boundaries, and not violently flooding every continent known to humans. Yet, if the world were to stop turning, the bulge would cease to exist and water would rush the Earth's north and south poles. Furthermore, loss of rotation most likely also means loss of magnetic field—and protection from potentially devastating solar winds. Eventually, it would be a matter of time until temperature, weather, oil and food supplies all became wildly out of order.
So to what degree should we worry about this phenomena? Probably very little, as NASA scientists predict such an event is extremely unlikely to occur, even within the next billions of years. Just in case, check out the amazing space footage and expert testimony in this playlist, complete with a full documentary demonstrating what the world would be like without its rotation.