It's linked to an old superstition that everyone is psychically linked to the piece of ground that will contain their body after death. The belief is that if a goose walks over the ground, you will feel a psychic 'shiver' - when the hair folicles in your skin contract - hence the term 'goosebumps'. The phrase has expanded in modern times to 'Someone has just walked over my grave' to explain a similar reaction.
I'm sorry but I think there's a simpler, more mundane explanation than that of Andy Hughes, above. The pimply appearance of flesh which is experiencing goose bumps, because of cold, fear etc, looks like the flesh of a plucked goose (or other bird). And if you feel someone's goose bumpy arm, in addition to the pimples, it has the same cold, clammy feel as a plucked bird.
Perhaps there's a clue in your nickname, Yankee. You see, 'goose bumps' - which first appeared in writing in the 1930s - was simply an American version of the older British word 'gooseflesh' to describe this skin condition. Of course, many of US have now adopted YOUR version! Even ours did not occur before 1810, so it seems rather late to have anything to do with grave-superstitions. Both refer to the plucked clamminess idea, as suggested by Geofbob above.
irresistible mental imaage o Buffy-style malignant vampire goose stalking graveyards....Afraid Geoffbob is correct. The things that werent suppposed to walk over your grave were far amore sinister...dun dun duhh!!!! WOMEN!!!!!
The wonder of the Answerbank! A simple explanation, which I dredged up from my subconcious starts a veritable debate - this is the site in action. Thanks to all who added to my original answer - as always I am delighted to stand corrected in view of the evidence contradicting my original premise.
yeah andy its all comes from being so darn confident about knowing everything. Go plucka goose, if that aint pimply enough for you, do it standing on someones grave...........