Absolute chaos.  Earth's core is made of spinning molten iron which produces our magnetic field that many species use to orient themselves and migrate.  We would also be bombarded by the solar wind which is intercepted by the magnetosphere and redirected to the poles to create the auroras. 

That would be a big "IF". For one thing, the pulse of heat given off would be enormous. "Suddenly" in such terms would be millions of years, more likely billions. I you could magically do it withing days, the explosive release of heat would be disastrous, and the sudden stoppage of rotation would cause global earthquakes to make the K-T dino-killer quake look like the New-Year firework display in London, rather than say in Taiwan.

As for tsunamis...

As for the magnetic effects, I don't take them seriously. They come and go every few tens or hundreds of thousands of years without leaving much fossil trace. Nor is there any reason why they should have more than nuisance effects.

It would be an interesting thing to try though, if anyone has any ideas...