A question similar to this was posed in the old Forums. But that question was only asking about stopping the Earth's rotation on its axis. For the current discussion, rotational velocity is negligible since, even at its worst (at the equator), rotational velocity is only about 1,000 mph. Orbital velocity is something just over 40 miles per second! But, as I said in the old thread, it depends upon the mechanism that does the stopping.
If it were done mechanically, we would have some serious problems, that's the bad news. The good news is that only a fraction of a second later, we would no longer have any problems at all . For people on the "leading" edge (whose clocks read after midnight but before noon) there would be a brief but very interesting ride, as they found themselves launched suddenly from the ground. Those standing on the equator at dawn would be launched straight upward, while those at the polls, along with those who have just past midnight or are just shy of noon, would be launched straight sideways. Now, I was going to add that all of these people would instantly be vaporized by their impact with the air, but the truth is the atmosphere would probably leave with them. So they would find themselves propelled into space, where the atmosphere would rapidly dissipate, and they would all spend the last few seconds of their mortal existence sucking vacuum (and all that goes along with that).
Those on the "trailing" side of the globe (whose clocks read after noon but before midnight) would make impact with the ground beneath their feet at 40 miles per second. They would not even be a stain.
However, if this were done by an anomaly of rotating space-time, it might be possible for the event to pass utterly unnoticed. With no catastrophic change in momentum, and no measurable acceleration forces, the event could only be detected through observation of objects not affected.
