Playing games on the phone requires a goal that is obtained mostly through speaking or questions. Games such as King's Cat, Would You Rather and Twenty Questions are suitable for this medium.
In the game King's Cat, one person chooses a letter of the alphabet. The next person says the phrase "King's cat is a ___ cat," filling the blank in with a word that begins with the chosen letter. Players take turns in this fashion until one player can't think of a word that has not been used. The winner is the last person to think of a word that has not been used before.
Would You Rather is a game in which two or more unfavorable scenarios are invented, and the person must decide which scenario they would rather do. There is no winner or loser in this game, but it can be a funny conversation starter.
Twenty Questions is a simple game that can include two or more. One person thinks of a person, place or thing. The other player or players then have the chance to ask up to twenty yes-or-no questions in order to guess what the other person is. The player wins the game by guessing the other player's person, place or thing before the twenty questions run out.