Guess Who is a classic board game for two players. It was a hit in my household growing up. A couple of few ago, we purchased is for our daughter who was five years old at the time.
There is a deck of cards with each card representing the face of one of the many persons on each players gaming piece. Each player draws a card. Then, players take turns asking yes/no questions in an effort to identify the opponents character by process of elimination. It's very simple to play, and further, very easy to teach young children how to play.
The game teaches young kids how to think and strategize using process of elmination. We have really enjoyed playing it with our daughter for the last couple of years. We purchased it shortly after our daughter began grade school. It turned out to be a great age to introduce the game.