Chess
Chess has been with us, in one form or another, for centuries. Scholars still debate from where we got chess, and even why it is called 'chess'. It is a very established game, and even those who don't know how to play, know what it is. Because it is ubiquitous, chess is a good family game. There is a global community of chess players, and an international body to rank players. One can find dozens of good, simple websites to explain the rules, and hundreds of books to explain the theory.