Some of the smaller electronic video games make good backpacking games, but you have to carry extra batteries. Some board games have light enough versions, like the cloth chess board and light plastic pieces that I occasionally carry with me, but then I need a flat surface to set it up on. In any case, being an ultralight backpacker, I prefer the games that don't add a single ounce to the pack. here are some examples.
Games Using Natural Items
There are a lot of games that can be set up quickly using natural elements available in the wilderness. Perhaps the simplest is the game Tic-Tac-Toe. Scratch two lines in the sand and two crossing those and you have your board. Each player can use a stick to make his marks. In sand the marks are easily erased in preparation for the next round.
If there is a large enough flat area with dirt or sand that can be smoothed out, there is another games that can be played with sticks for pencils. Make a grid of lines roughly ten by ten, and then in the boxes created write the first letter of your name. Your opponent will then do the same, with the object being to get five of your initials in row.
Not all backpacking games need to be mental games. You can have a lot of fun with simple tests of coordination and throwing ability, for example. Just create a circle or square two feet across, and toss pine cones at it to see who can get the first one to stay inside the target, or who can get the most out of twenty to stay in it. If there are no pine cones, use rocks or pieces of wood or sea shells.
In the winter you can of course have snowball fights. But if you prefer not to get wet and cold, you might have a competition that involves hitting a tree or other target. Competitive building of snow shelters can be fun as well, and it will help you train for survival, just in case.
Games That Require No Materials
Some of the best backpacking games don't require you to either carry pieces or gather natural materials. These are the purely mental games that will balance the physical exercise with some mental training. For example, there is the game where you say a word and then your opponent has to say one that starts with the second letter of the one you used. You then have to do the same, and so on, until one of you cannot find a word within fifteen seconds or so, and so loses.
There is a good mental exercise that will also train you in the right frame of mind to deal with wilderness emergencies. Start by choosing any item in the wilderness around you. Then find survival uses for it in your minds. For example, if it is a log, see how many ways you can each think of to use it in a survival situation. You can play this as a competition or a collaborative effort.
Other games that can boost your wilderness skills include ones like guessing how long it will take you to get to some distant landmark. You might also try to identify as many plants as you can while you are hiking, and recall which are edible or useful. Nothing to carry, nothing to gather, and they can be played anywhere - these may be the best backpacking games for those who like to keep it light.