The probability for such an event is practically
zero in the next few billion years. If the Earth stopped spinning suddenly,
the atmosphere would still be in motion with the Earth's original 1100
mile per hour rotation speed at the equator. All of the land masses would
be scoured clean of anything not attached to bedrock. This means rocks,
topsoil, trees, buildings, your pet dog,
and so on, would be swept away into the atmosphere.
If the process happened gradually over billions of years, the situation would be very different, and it is this possibility which is the most likely as the constant torquing of the Sun and Moon upon the Earth finally reaches it's conclusion. If the rotation period slowed to 1 rotation every 365 days a condition called 'sun synchronous', every spot in the Earth would have permanent daytime or nighttime all year long. This is similar to the situation on the Moon where for 2 weeks the front-side is illuminated by the Sun, and for 2 weeks the back side is illuminated. This situation for the Earth is not the condition of 'stopped' rotation, but it is as close as the laws of physics will let the Earth get.
If it stopped spinning completely...not even once every 365 days, you would get 1/2 year daylight and 1/2 year nightime. During daytime for 6 months, the surface temperature would depend on your latitude, being far hotter that it is now at the equator than at the poles where the light rays are more slanted and heating efficiency is lower. This long-term temperature gradient would alter the atmospheric wind circulation pattern so that the air would move from the equator to the poles rather than in wind systems parallel to the equator like they are now. The yearly change in the Sun's position in the sky would now be just its seasonal motion up and down the sky towards the south due to the orbit of the Earth and its axial tilt. As you moved along constant lines of Earth latitude, you would see the elevation of the Sun increase or decrease in the sky just as we now see the elevation of the Sun change from a single point on the Earth due to the Earth's daily rotation.
For example, if you were at a latitude of +24 degrees North in the Summer and at a longitude where the Sun was exactly overhead, it would slide gradually to the horizon as Fall approached, but since the Sun has moved 90 degrees in its orbit, it would now be due west. Then as we approach Winter, you would now be located on the dark side of the Earth, and would have to travel in longitude to a location 180 degrees around the Earth to see the Sun 1/2 way up the sky because in the Winter, the Sun is 48 degrees south of its summer location in the sky. It's a little confusing, but if you use a globe of the Earth and orient it the right way, you can see how all this works out.
As for other effects, presumably the magnetic
field of the Earth is generated by a dynamo effect that involves its rotation.
If the Earth stopped rotating, it's magnetic field would no longer be regenerated
and it would decay away to some low, residual value due to the very small
component which is 'fossilized' in its iron-rich rocks. There would be
no more 'northern lights' and the Van
Allen radiation belts would probably vanish, as would our protection from cosmic rays and other high-energy particles. This is a significant biohazard.
From Ask the Astronomer
Copyright 1997 Dr. Sten Odenwald