Pole shift

Pole shift is the hypothesis that extreme movement of the Earth's rotational axis occasionally occurs and can explain catastrophes such as earthquakes and tsunamis. This phenomenon refers to a change in the geographic location of the poles and is distinct from plate tectonics, geomagnetic reversal, and change in axial orientation. Significant shift has not occurred for at least 800 million years and often occurs over periods of thousands, if not millions, of years. A slight pole shift over time is normal and harmless; for example, the effects of precession where the angle of the rotation move around like a gyroscope over a cycle of around 26,000 years.

This, of course, is an attempt to piggyback off (and mimic) the cool science-sounding terminology related to shifting poles. The fact that most cranks willingly conflate the concept of a magnetic pole shift with the cartoonish idea of the sudden physical inversion of the Earth's rotational axis only sweetens the deal.

Predictions
In 1997, a rapid pole shift was predicted for 2000. Unsurprisingly, this did not happen.

In 1996 a pole shift was predicted for 2001. This did not happen either.

The 2012 pole shift didn't happen either.

See the pattern?

Comparison to geomagnetic reversals
The Earth's magnetic field can flip. This is called geomagnetic reversal. But these magnetic-pole reversals haven't been correlated to any widespread disasters, such as volcanoes, earthquakes, tornadoes, or the dead rising from the grave, so it appears to be nothing worth getting that worried about. Also, they happen over a period of thousands of years, not suddenly on a given date — so whenever you hear a claim that a pole shift will occur on a specific day, you know not to believe it.

Actual pole shift in the Solar System
Mars is thought to polar shift, like Saturn's moon.