I am assuming that the atmosphere retains its velocity here.
At the equator, the surface of the Earth moves at around 470 meters per second, so this would correlate to the kinds of winds you would see once the Earth stopped spinning (if it did so immediately). Nearly everyone on the surface would die due to the amount of debris flying at a little over a thousand miles per hour. The wind would be highest at the equator, obviously, but everyone between 42 degrees north and 42 degrees south, about 85% of the world's population, would experience these kinds of winds.
If your characters were in a subway or some other subterranean tunnel when it happened, they might be fine. For example, there is a network of tunnels in the bedrock below Helsinki, Finland that includes a shopping mall, hockey rink, swimming complex, and even more.
That would most likely be the best place to be when it hit. No building on the surface would survive, except maybe at the South Pole; not for long though.
The kinetic energy of this supersonic wind would quickly heat up the air once it was over, and in areas where the air is moist, there would be huge thunderstorms the like of which we haven't seen before. The equator would pretty much be uninhabitable at this point, even if you were a hundred feet underground.
The temperature would be thrown off by this extreme heat, the cold water below the oceans' surface churning up a mix of wind, spray, fog, and of course, rapid temperature changes everywhere.
The low oxygen water would kill off many of the ocean animals, and any animal that needs to breathe, like dolphins and whales, would have a very hard time doing so in the sea spray.
The sun now rises and sets every once a year, so day and night respectively would be six months long for everyone.
The moon has not stopped spinning around the Earth, however, so months wouldn't change. You'd just have six months every day and every night.
Eventually, though this might not apply to your story, the Moon would accelerate our spin, and its gravity will slowly tug on our planet and get us back into action. It would no longer have tidal energy to supply it, and since right now, the Earth spins faster than the Moon, and our tides slow down our rotation while pushing it away from us, so that would be reversed, and we would finally start spinning again.
—Most of this I got from the book "What if? Serious Scientific Answers to Absurd Hypothetical Questions", which is an awesome book to get a good laugh out of while learning something interesting.—
I can't find it on his site, but here is a version that Google turns up. To summarize,