My mother has moved just about once for every year of her life. Actually, prior to moving where she is now, I think it was almost exactly that. Speaking from her experience: it sucks all the balls. You never really feel settled anywhere, or like anywhere is home. As you grow older, even if you move about all over the place yourself, if you've built up friend and family connections in one place, that place will always be your "home base". My mother hates that she doesn't have that - the closest she has is "southern England", because that's where our (massively extensive) family all pretty much exclusively live. It also means that the only friends she's ever had consistently are her cousins and stuff. She has had friends for long periods of time, admittedly, but never for longer than a decade, really.
I'm lucky in that I had a relative amount of stability while still moving about a little to get used to it and such. I lived in Hong Kong and Germany as a baby, but don't really remember it. The moves I remember are from southern England up to Scotland, moving house once in Scotland, and then moving down to London for university. Nothing too major, but enough to get me used to the idea of a fluid sense of home, location, culture, etc. etc.
As for stories about moving... uh, probably the best one is me finding the used heroine needles in the bottom of our flat's stairwell on moving day, when we moved to our second place in Scotland. Turned out there was a needle exchange round the corner (addicts can anonymously go to get sterilised needles to try to cut down on blood-transmitted disease), so the dealers would wait in the little old crooked alleys and lanes nearby that inevitably permeate the centre of an old city like Edinburgh. Addicts would go, get the needles, meet the dealers, and then break into flat stairwells to shoot up out of sight. My mum used to have to chase them out with a baseball bat. (Note: don't ever mess with my mum.)