That just talks about the Staunton design for individual pieces: how to tell a pawn from a bishop etc. The question here is about the starting layout, which is almost unchanged since 5th century BC. (Kings were not on same file originally.) As previously mentioned, names and movement of most pieces did change at various times, so it's a question for the philosophers as to whether it's really the same layout now.
Why are chess pieces laid out like this?

It's nothing to do with the powers of the bishops and queens though - the placement goes back to the parent game when the bishop was a (2,2) leaper (fil) and the queen moved one square diagonally (fers). Of course in many languages they aren't called "bishop" or "queen".
This is actually the most accurate answer so far.
In the older version of the game, the bishops (called elephants originally) could only move 2 squares at a time - no more, no less. If they started where the knights are, there wouldn't be room for them to move 2 squares towards the edge of the board. Their starting position makes sense when you think about that. In XiangQi (Chinese Chess), the elephants still move that way, and start in the same position as in western Chess.
XiangQi also has two advisors instead of a single queen, starting on either side of the king and only moving one square diagonally. This is similar to the original version of the queen in western Chess, just with two of them that work together instead of just one.
Interestingly, the knights (horses) and rooks (chariots) in XiangQi are exactly the same as in western Chess, except that the XiangQi horses can't jump over things like the knights in Chess.
I found it very interesting when I first learned to play XiangQi to compare the back row pieces to western Chess, as the similarities and differences tell you a lot about the common ancestral game that they both came from.
I guess it was considered obvious that the King and General had to be in the center of the army to effectively command it. Because the Bishop was originally an Elephant, a piece that jumped two diagonally, swapping Elephant and Knight would make them compete for d3/e3 as natural development square, making opening play quite awkward. Starting a Knight or Elephant in a corner gives them only very few choices for a first move, so the Rook is sort of a left-over to go there (as it doesn't really mind).
An interesting detail is that originally the Kings started on d1/d8, in the Arabic/Persian precursor of Chess, ('Shatranj'), and the Ferz ('General') on e1/e8. Then there appeared a medieval game Courier Chess, on a 12x8 board, where the Ferz was still standing right of the (white) King, but on the left of this King was a non-royal piece that moved as King, where Ferz moved only one step diagonally. (And the Bishops were introduced as new pieces standing inward next to the Elephants.) The non-royal piece moving as King later evolved into our modern Queen, by extending its range. (Hence modern Chess was originally known as the "Mad Queen variant".) But it has always kept its position left of the King, even on 8x8 boards.
I think the placement has a lot of metaphor. clearly the king and queen are placed next to each other as family. next surrounded by their spiritual council, the bishop. next protected by the knights. lastly they are all enclosed within the walls of the castle, the rooks.
I guess this was the main reason for the current names and shapes of the pieces to become popular. But the same setup already existed when the Rook was still named 'Chariot', the General was not expected to have any family ties to the King, and Elephants were not really the first animals you would turn to when in need of council...

The King can do no wrong, so the Queen is allways to his left.
Yes, except in the case of black pieces. The queen is to his right.

Then there's Burmese Chess, where only the pawns have a fixed initial placement and all the pieces are played from hand one at a time - and can still be switched around freely after they're all placed - until a pawn moves or anything is taken. The pawns are placed on the 3rd and 4th ranks initially (the right half of each player's eight on the 4th rank, the rest on the 3rd) to leave deployment space behind them.
--That's how I first heard of it, but the Wikipedia article varies slightly from the book I read 40-odd years ago.
Maybe this will help.http://www.chess.com/groups/forumview/how-the-chess-set-evolved-to-what-we-know4