Mastermind is an easy-to-play mystery peg game.  One player places pegs of given colors in a secret "compartment", while the other tries to guess it.  They get clues after each guess; the other player reveals how many were the right color and how many were also in the right spot.  It's a little tricky at first, and if the person who sets the pattern makes a mistake, it can be frustrating.  This is limited as a family game because it only involves two players.  Ultimately, this is best for two people who enjoy mind problems.