Why are the boards not square?
The design of Go components is all about symmetry.  Because perspective shortens the vertical height of the board, the boards are made taller than they are wide.  This way they appear to be square when you're playing.  Another similar issue occurs with the stones.  Black stones appear to be smaller than white stones, so the black stones are actually made slightly larger than the white stones to counter this effect.

Related and awesome: How many squares are there on a Go Board?