The Bishop or the Knight?

Which piece is better; the bishop or the knight?  Walk into any room with amateur chess players and everyone will know.  Or so they think.  The evidence they present for their case is neither concrete, nor valid, but it's enough to make them believe it.  I've heard everything from "The bishop moves farther" to "I just like the knight more."  I've even heard that both pieces are always equally valuable because they're both worth three points.

The truth is that one is better than the other, BUT that depends entirely on the game being played, and the way the pieces are being used.

The bishop definitely has more range.  Placed on the a1-h8 or a8-h1 diagonals bishops can cover a vast eight squares in a single move.  None of that range matters, however, if the center is closed.  The knight, on the other hand, thrives in these "closed" positions.  They don't have the range of a bishop, but they are the only piece that can jump over other pieces.  That means that in closed/cluttered positions they can simply jump over pieces whereas the bishop had to get through them.

In a position like the one above, where pawns are obstructing the center of the board, bishops simply can't move around.  It's not much use having a piece with all the range in the world if it can't move.  The knights on the other hand are incredibly active and will not be easily chased off of their posts.

Bishops thrive in positions where the center is open.  In positions like these they can capitalize on their range and wreak havoc over long distances on the board.  Knights don't do so well in positions like these.  Their ability to leap over pieces is made less valuable by the fact that their movement is so slow.