The Earth spins because of a large body that collided with the planet billions of years ago during its early stages. This resulted in a spinning earth as well as a friendly neighborhood moon.  Originally the days were 6 hours long. Gradually the Earth and the Moon settled gravitational relationship with the Moon’s gravity causing tidal waves on Earth. Friction caused by the tide act as friction and is able to slow down Earth's rotation over a period of billions of years. The laws of physics however, will not allow the Earth to completely stop.  

However, what if, hypothetically speaking, the Earth spin did stop. The Earth’s rotation and its distance from the Moon affect the length of day, the seasons, the tides, as well as the wind patterns. Without a spin, the Earth will have 6 months of sunlight and 6 months of night time. As a result the days will become hotter and the nights will become colder especially towards the poles due to the tilting of Earth. As a consequence, the global wind patterns will change to  North-South, as wind moves from the cool equator to the hot poles.

More interestingly, the oceans will migrate towards the poles as a result of the stopped rotation leaving a mega continent near the equator with potentially the right temperature to support life. However, the stopping of the Earth spin will result in layers that move at different rates which would cause friction, earthquakes, and volcanic eruption until the core stops spinning. With that occurring, the Earth would lose its magnetic field and become vulnerable to deadly solar radiation. If that did not destroy all life then the lack of a sunlight would start its destruction from the bottom of the food chain where phytoplankton resides which heavily depend on sunlight and warmth.

With all that being said, there is nothing to worry about. During the past 100 years the Earth rotation only slowed down by only 1.4 millisecond.