Scrabble
Scrabble is a perfect game for two people. It challenges both players to come up with words using letter tiles and arrange them on a board crossword-style. Be sure to have a dictionary handy for looking up and verifying words. Scrabble is not a quick game because of the mental strategy, but it will keep both players entertained and on their toes.
Battleship
Battleship provides each player a game board mapped out with a grid. Players decide where to place their ships. They take turns guessing where the other player has placed their ships, and the first player to sink all of her opponents' ships wins. There is little mental challenge to this game, but it can be played by children and adults.
Cribbage
Cribbage is a card game that uses a game board marked with small holes. Pegs are placed in the holes to keep score. Each player moves his pegs as he accumulates points based on card combinations. The first player to accumulate 121 points wins. A shorter version of the game sets the goal at 61 points.
Slap Jack
For the younger crowd, the card game of slap jack is always fun. There is no thinking or strategy involved. Each player is dealt cards face-down. One at a time, each player places his card on a central pile. When a jack is played, whichever player can slap the jack with his hand first receives the jack and all the cards underneath. The goal is to obtain all the cards. Players with quick reflexes do well in this game.
Checkers
Checkers is played on a board marked with red and black squares. Each player has a set of checkers in either red or black. Players take turns moving their checkers across the game board. The strategy is to move your checkers to capture the other player's game pieces quicker than they can capture yours. If you find that checkers is not challenging enough, consider playing chess.
I'm Thinking of Something
This is a wonderful choice for children and adults. One player picks an object and commits it to memory--it could be an item in the room or something as vast as a landmark. Once she has selected her item, she provides a clue to begin the game. If she selected a car, for example, she could start by saying, "I'm thinking of something large." The other player asks "yes" or "no" questions until she has enough information to make a guess. She shouldn't make a final guess until she's quite certain she's right. If her guess is incorrect, she loses the game.