If Earth stop rotating or to reverse its rotation, it would be catastrophic for the Earth in almost every possible way! I think I'll just list some of the things that might happen:
If the Earth's rotation INSTANTLY stopped, everything not fixed to the Earth would continue to rotate around at the same velocity that they were before due to conservation of momentum. To us it would feel like a giant earthquake where the Earth would suddenly start "moving" in the opposite direction of the rotation. Buildings would collapse, the oceans would wash up onto land in large tidal waves, and there would be a large atmospheric wind shear at the surface. (The atmosphere is not attached to the planet either and would keep rotating too). Since we are traveling at about 460 m/s at the equator (about 1000 miles per hour) we would be tossed pretty far. (We wouldn't fly off the earth, though. Escape velocity is much higher.) As my officemate said when I told him about this question "We would be thrown into the wall at 1.5 times the speed of sound as the building was tipped off its foundation."
Seismic waves from the impact would travel through the earth causing massive earthquakes. Depending on the size and velocity of the impactor, the earth might even break apart.
Much of the atmosphere would be boiled off. A fireball would expand outward destroying material in it's path and polluting the rest of the atmosphere. Those things would probably kill all life and level everything on the Earth's surface! It would be much worse than the extinction event that may have contributed to dinosaur extinction. If we were magically able to stop the Earth with no bad consequences, life on a non-rotating or retrograde (backwards) rotating planet would be very strange.
On a retrograde rotating planet, the sun and all the stars would rise in the west and set in the east.
If the rotation was very slow, the day could be very long. This would have a huge effect on plant and animal life on the earth, some of which could not survive many days with no sunlight.
If there are any physics enthusiasts out there, from knowledge of the mass of the earth, the radius of the earth, the earth's escape velocity (use as impactor velocity), the rotation period of the earth, and the average density of the earth you can calculate a very rough estimate of the size of an impactor needed to stop the earth's rotation. If I assume that the earth collides with an object just sitting in its orbit right at the edge at the equator I get a rough radius of 1600 km for the needed size. In reality, you would probably need something much, much bigger. There are not any objects of this size in the solar system that we don't know about, which means that this scenario can't really happen.