For younger children, basic puzzles, such as those made out of wood, can help children learn hand-eye coordination, basic motor skills, as well as factual information about the world around them. For these children, puzzles featuring items such as the alphabet or numbers work well; for younger children, search for puzzles with a smaller number of pieces, which will then be larger, to help them master these basic skills. Older children can handle more delicate cardboard puzzles, which, when constructed, can also be educational: these puzzles might feature maps of the world, US presidents, or other pieces of important knowledge. Alternately, you can find puzzles that, when constructed, offer a brainteaser, combining two forms of education into a single game.
For any child who can already read and write at a basic level, word puzzles make an original way to reinforce these skills. For younger children, word searches with basic words will work well; to help them build their vocabularies, construct or search for word searches with a variety of vocabulary words all in the same group (such as food, or countries, or other categories). Older children can also do word searches, though crossword puzzles are more likely to challenge them, testing their factual knowledge and recall. Crossword puzzles can also make an interesting alternative to a quiz on information and facts the children have studied in class.
To help reinforce spatial reasoning, mazes provide children with the opportunity to determine how to get from point A to point B. Older children can handle more complicated mazes, or even construct their own and exchange papers. To make mazes more of a challenge and provide additional education, construct "roadblocks" along the path in the form of math problems or basic questions about material you've already covered; students must answer the question to be able to bypass these roadblocks and continue on the maze's course.
Brainteasers and riddles also help develop children's critical reasoning skills, while intriguing them with the mysteries in front of them. To make brainteasers more challenging, think about different ways of phrasing basic facts. For example, a riddle about an American who can't go any further north while staying in the same country might depend on the fact that the American is currently in Alaska. Make sure not to construct a brainteaser that features information your child has not yet learned in order to avoid frustrating him or her -- though complicated logic (rather than unknown facts) can present a challenge that is satisfying to overcome.