Classic games like Monopoly, Risk, and Clue are generally more fun to play than games that are marketed as "educational." If the game were any fun, it would sell on its own, educational or not. But, that's not to say that Monopoly doesn't teach volumes about capitalism, or Risk about geography. My son never gave a hoot where Scandinavia was until he had to defend it against an advancing horde.
Any game can be educational, if you approach it right. For example, just consider...
Trouble, that Pop-a-Matic game from Milton Bradley, probably isn't the first thing you think of when you think about moral theology. Yes, it's a good counting game. And, the toddler can't swipe the dice and swallow them. But, it can also be a great ethical teaching tool with kids as young as 4 or 5. You see, this game has lots of opportunities for envy, revenge, anger, and other wicked behavior, and it also has chances to show mercy and forgiveness. You don't need to be preachy about it, but neither do you have to leave all that stuff behind in the Sunday School classroom.
For example, your daughter may be trapped on home base while everyone else sails around the board. If she pitches a fit, you could say, "Aw, don't be a crybaby," or you might think better of it and say, "Envy is really hard, isn't it? It hurts to see others getting a better break than you." It's one thing to talk about envy in a classroom, and quite another to be suffering it at the moment.
Or, your son may have the choice of sending your peg back to base or moving another piece instead. You could say, "Don't you dare send me back, you little monster." But, the more thoughtful response might be, "If you show me mercy, I'll be more likely to show you mercy when it's your turn. But, if you don't show me mercy, don't expect any in return."
And, what if your only legal move is to send your kid's peg back to base? You can provoke a tantrum by saying, Ha! Gotcha," or, you can say "I had no choice. I'm sorry. I really don't want to start a war." Your child may well respond with sympathy instead of anger.
Any time the kids spend playing chess, checkers, Connect Four, Clue, Scrabble, or Mastermind counts as school.
Mancala is a generic term for a whole family of games, and there actually is an Arabic variation called "Mancala." However, hardly anyone plays Mancala on a Mancala board. Mostly they play Oware or some other game. Math Blaster 1st Grade teaches the Arabic Mancala game. Your kids may be surprised to find out that very few people they meet play by the rules they know. Be warned.
Lately, we have been trying to have family game nights, and one of the best games for mixed ages is Rummy. If you think about it from an educator's viewpoint, it's amazing how many things kids can learn from a good card game:
...all from playing Rummy!