In our world, mountains generally only move up (while forming) or down (while eroding or sinking). Otherwise they follow the tectonic plates they happen to be on. In island chains like the Hawaiian archipelago it may seem that they are moving but actually some plate is moving apart from another one, with the islands form at the boundaries.
Would it be possible to have an actual moving mountain, though? I'm thinking of mountains that move over the tectonic plate they are on. In any direction other than up and down, at any speed - it doesn't have to be something noticeable on a lifetime, or even over millennia.
The reason I'm asking is because I dreamed about a mountain that circled its world every couple hundred million years, leaving paleonthologists and geologists baffled about the fossils and formations on and in it.