Chess
Play chess with a friend, with a clock or without.
Start a game, pick a time control and invite a friend. You play white, they play black. Drag a piece to move it, or tap it and then tap a square. Each of you gets a notification when it is your move. The game ends in checkmate, stalemate, a threefold repetition, the fifty-move rule, a flag on the clock, a resignation or a draw you both agree to.