Will the Earth ever stop rotating?
The short answer is "Probably Yes".

The longer answer is that it is debatable whether Earth's rotation will become tidally locked to the moon due to tidal drag, at which point it will not be rotating relative to the moon, or whether the sun's exhaustion of hydrogen and the fusion of Helium will result in the sun's expansion vaporizing the earth first.  As tidal drag slows the earth's rotation, the moon moves further away, reducing its effect on the earth's rotation, and making the calculations fairly complex.

In either case, unless something really unexpected happens to the earth first, such as it being ejected from the solar system, which is completely improbable, it will stop rotating, if only due to it ceasing to be a planet at all.