Ticktacktoe
Ticktacktoe is a strategy game you can play over the phone. Each player needs a sheet of paper on which to draw a ticktacktoe board, which is two horizontal lines criss-crossing with two vertical lines, making nine squares. Starting from the top left square go across and label each square 1, 2, and 3; in the next row continue across with 4, 5, and 6; then at the bottom label 7, 8, and 9. Player one will go first and mark an X in one of the squares, informing the other player which square he placed the X in by its number, so that player two can mark it off on her board accordingly and make the next move.
Twenty Questions
Twenty questions is a popular guessing game that you can play over the phone. Player one starts by thinking of an object, person or place. Player two gets to ask any questions she wants in order to get clues about what player one is thinking about, until she has asked twenty questions total. Each time player two asks a question she can try to guess the object based on the answers she's acquired up to that point. The goal is to guess the object player one has thought up before reaching twenty questions.
Guess the Noise
Guess the noise is another guessing game you can play on the phone that challenges players to get creative with the noises they make. One player will make a noise using an object he has available to him, and the other player must guess what is making that noise. For example, you can play with the noise a soda makes when you open it, tapping a glass with a knife, rain outside if it's raining, a toilet flushing, or any other number of noises you can make with household objects.
Chess
Chess is a convenient board game to play over the phone with someone, as standard chessboard spots are labeled with a letter and number. Players each set up a chessboard and pick a side. Each time a player moves a piece she tells the other player the square she moved her piece to, so that the other player can document it on his board as well. This can also be done with checkers.
Telephone Pictionary
Telephone pictionary is a drawing and guessing game that allows for a little imagination. Player one will think of an object or person, keeping it simple and not too complicated, at least at first. Player one will then try to describe to player two how to draw the object on paper, and player two will attempt to draw and guess what it is based on player one's instruction.