Chess Board graphics - This is a collection of really nice chess board type graphics, put together by nick.cash.
Squidi's 300 (or so...) - This has been posted a number of places already, but there are a few really interesting ideas on there that are easily adaptable to a Byond board game.
About.com's 8x8 board game contest - These games were designed to be played on an 8x8 board. While it might not be a good idea to build a game exactly like one of these, they can provide ideas for creating a game of your own. ManoAMano was inspired by Robo-Battle Pigs, which was itself inspired by something called Richochet Robot.
Board Game Geek - The biggie. Huge piles of information about all kinds of board games. Usually the first place to look for board game information.
D'Antiques Game Rules - Links to .pdf or .html rule sets for over 700 mostly board games.
Well, that's a start. If you have a favorite resource you would like to add, reply to the appropriate post in the Resources forum: Graphics, Inspiration , or General.