http://jd2718.wordpress.com/2007/04/21/puzzle-how-many-rectangles-on-a-chess-board-solutions/
1296
Including squares, 1296.
Assuming you are asking for the movement squares and not the board or any combo of the movent squares, 49.
There are infinitely many such rectangles.
That depends on how big the rectangles are.
Rectangles and squares both have 4 corners.
4 rectangles
96 rectangles.
There are 15 rectangles.
2 triangles and 3 rectangles(:
There are 2025 rectangles in a 9x9 grid.