No, the grain of the wood always runs the length of the instrument. It's just that many (not all) makers use what is called "curly" or "flamed" maple for the backs. The "flames" are the result of figure in the grain and are visible as pronounced stripes running at right angles to the grain. The sides are usually made of this wood as well and you should be able to see the figure running across the width of the sides from back to front.

      - Mark