Something we did in the Boy Scouts: bring game boards (what?) No, listen. If you carry a sleeping pad, you can use a Sharpie and ruler, make a checker/chess board, backgammon, Chutes & Ladders, etc. Then you just carry what you think you need, like the chess pieces or dice. You can use rocks vs. sticks if you're a checkers player. I've never played backgammon...
Even if you don't carry a sleeping pad, you could use pretty much anything flat, eg your space blanket. Or just get a piece of paper, use both sides for different games, and get it laminated. Fold it up and forget it.