We would have to rely on video - rather than a simple transcription of the moves.
The longest move in time rather than space would be a horse of a different colour. Asimov's epic 14-volume Foundation & Empire trilogy revolved around a somewhat similar enigma: where are the opposite ends of a chess board?
If you can afford a Microsoft Surface for scientific purposes (or build a simple 8x8 touch-sensitive board), and write some software to stack the results, you could provide exact results, get a subvention or two for it and sell the result to chess board companies 
You'd need to play 50-100 games on it, keep the rating of the players, and you'll be able to say "players between 800 and 1200 do less pounding but more scratching than 1200+" for example. And to top it all, create a geeky graphic and sell that to Wired!
This will certainly yield more precise results than simply looking at moves.
Oh, and while we're to build a bridge when we want to cross the road, note that most players will place pieces to "look" forward, so you may want to "protect" the "front" of the pieces foots with soft material; it'd be nice and protective, and if you're an engineer then create a new material that is stronger in one direction.
Oh, and if you can build it so it follow's NASA regulations and add some magnetism, astronauts could play chess in space!
Oh, and... oh, nobody's listening to me, right? Okay, okay...
huh, i don't understand... ;(
What is the greatest distance travelled by a single chess piece in the course of an actual game (in terms of chess squares)? It should be possible to calculate it from the move history.
... The winner of the greatest number of squares travelled by a chess piece is therefore: the KNIGHT! travelling 5 squares.
Artfizz I only wish you had asked this question a long time ago as by now it would be common knowledge. ...
What is the greatest distance travelled by a single chess piece in the course of an actual game (in terms of chess squares)? It should be possible to calculate it from the move history.
Artfizz,
So what is the precise question that you asked?
Did you not ask: "What is the greatest distance travelled by a single chess piece in the course of an actual game (in terms of chess squares)"
This is what I answered!! What is it you are looking for as many other people are likely stumbled as I am. I have answered based on an average game what number of squares a piece is likely to move as you asked and I intentionally put numbers that do not not add up to the 28 moves played by one side just to see if anyone would spot my incongruence, and no one yet has spotted it.
Perhaps my original question not sufficiently unambiguous. Consider this short game fragment:
1.Nc3 h6 2.Nd5 h5 3.Nf4 h4 4.Nh5 h3 http://www.chess.com/explorer/index.html?id=1258064&ply=8&black=0
How many squares are on the knight's path? It must be a multiple of 3. In this case, the answer is 12.
Depends. Did the horse jump - or was he pushed?