10x10 boards are in common use for international Draughts. E.g. http://www.raindroptime.com/checkers-and-draughts/checkers-material/checkerboard.html .
Nice wooden pieces of unorthodox shapes can be obtained from http://www.superschaak.nl . As Musketeerchess will shortly inform you, House of Staunton also sells several unorthodox plastic pieces.
Where on earth can I purchase different size boards (such as 6x6, 10x10, or 12x16 tile) online? Or even anywhere in general for that matter? I have been interested by chess variants lately and am struggling to find a way to play them.