I imagine we'd all be flung off into space at tangents to the Earth's surface. Assuming some magic force which grabbed the planet and just stopped it cold, without affecting anything on the surface, of course.
No.
The Earth is rotating with a tangential velocity (at ground level) of about 1100mph.
If it (the rock) suddenly stopped rotating, animals, buildings, people and the atmosphere would still be moving at this speed. Essentially you and everything else would be tossed at 1.5 times the speed of sound in to the nearest building, or mountain.
You would not end up in space, because escape velocity for Earth is far far higher than this, at around 25000mph. So you'd fall back to Earth, and if you hadn't already slammed in to anything, the fall from several miles up in the air would undoubtedly kill you.
Additionally, the atmosphere and seas would be moving at this 1100mph speed too, so there'd be tsunamis thousands of feet tall and hurricanes of the kind we've never seen before.
Anything not anchored to the bedrock would be destroyed. Plants and trees would be torn from the ground. Topsoil would also be thrown in to the air.
It would undoubtedly be the end for multicellular life.