The earth is good to spin for another billion years. There is no possibility that the Earth will suddenly stop spinning anytime before a billion years. Chances are good that other occurrences, such as the sun swallowing the planet, will happen before that. But let's just assume for a moment that the Earth suddenly stopped rotating. What would happen?
Here's an excellent video that beautifully depicts the chain of events that will impact the planet and life, if it stops spinning.