I deleted my original bone-headed answer which failed to take a few minor details into account. This is tougher than it looks at first glance!
How many squares on a chessboard?

Must they have the same orientation as the ranks and files, or can they be formed by joining square corners (or centres) diagonally?

Actually, it's 205.
The 204 mentioned, and the board itself. There is a border, whether it be an area with 1-8 down the side and a-h across the bottom, or just a design that may be half a centimeter thick or a couple of inches think.
So there are 204 in the 8x8 play area, and the board itself, so it's actually 205 Squares.

The 204 number includes the large 8x8 square. A border cannot be assumed.
I agree.
The answer is 204.

64 x 1x1
49 x 2x2
36 x 3x3
25 x 4x4
16 x 5x5
9 x 6x6
4 x 7x7
1 x 8x8
204 total, 206 if you count the squares in the chairs on either end of it.

What if it sits on a chequered tablecloth?
The question is how many squares there are on a chessboard, so that wouldn't matter.
... Unless you put the checkered tablecloth on the board...

The c4 square fell off of my chessboard. It really sucks for the light-squared bishops.
lol especially for white's light squared bishop
I am NOT just counting 1x1 squares, also 2x2, 3x3 etc. First correct answer gets a trophy!