In reply to mick taylor:
One vote against Settlers of Catan. The game is decided at the beginning, and the only thing you can change by strategey is how long you want to drag out the inevitable conclusion.
I think the very best board games take a well known, easy to understand game layout / rule set and manipulate it in a specific way to make things more interesting. Good examples include
Cat Attack (you can move your opponent´s cats and get them into trouble /run over by the car that moves around the edge of the board rather than moving your own cat to steal the fish, milk, and cat food),
Cosmic Encounter (every player draws a card that allows them to bend the rules in a different way, e.g. one may be allowed to move twice every round, the next one to look into their opponents cards, the third one might enslave or remove one opponent piece per round... Since there are many more rule bending cards than players, the mix will be different every time, forcing you to adapt your strategy),
or the ultra classic German Hexentanz (roll dice to move your pieces once around the board and then back into the house. As a complication, all pieces look the same and are only marked at the underside, so keeping track is almost impossible).
Chess, Go, and Backgammon are also great choices!
CB