Our Basenji we have had since a pup. He's always had this thing that if we hold him or pet him a lot he will literally shake off after he is down on the ground. He also does this periodically when we walk him for no reason.

What on earth? Do other B's do this or dogs in general?

I think dogs do this for various reasons. Depending on context, it can be "whew, glad that's over!" to "well, that was fun, what's next?". At any rate, not unusual, IMO.