There are lots of fun board games to play but if I have to choose one, I will choose Jenga. I am not really sure if it can be considered as a board game because it does not involve any board but I find it most interesting.
Jenga is a game played by two or more players. The players stack the blocks to form a rectangular structure or tower. The game is played by removing a single block with one hand by the players without causing the structure to fail and fall and putting it at back at the top of the tower. The person who causes the tower to be destroyed losses and the last person remaining wins.
I find it really interesting because the game requires some serious skills. First, the person must possess good analytical skills wherein he should be able to choose which block to remove wisely and in what way will it be removed. It is very difficult when you have shaky hands and when you move in really slow pace. Second, the game requires strategy. To be able to win, you should defeat your opponent by making moves that will make the game more difficult for the other player. By this I mean, moving blocks in such a manner that the next move he makes will cause the tower to fall down.
Among other board games aside from jenga, I also find scrabble interesting because it requires knowledge about words and techniques how to win the bonus points. There are plenty of other fun board games too like snakes and ladders and monopoly. I hope my answer helps!