Favorite Things
Use your time on the phone to play some type of question game. Question games can be a way for you and your girlfriend to learn new things about one another and find out what you both already know. Come up with lists of questions for each other that ask for things you think she should know about you. For example, your favorite band, ideal romantic date or favorite sports team. Take turns asking each other the questions about one another and keep score. Whoever ends up getting the most right answers about the other person wins.
Trivia Games
Trivia games are another activity that you can play over the phone with your girlfriend. You can either use game cards with questions from a board game you might both have copies of or come up with trivia on a variety of topics that you both have some knowledge of. There are also websites you can visit to find pre-made lists of trivia questions. You could even turn the game into a way to study for an upcoming test. Before you play, come up with a set number of questions so the game has a definite end point. Take turns asking each other the questions and keep track of the score. You may choose to ask open-ended questions or use multiple choice answers.
Online Games
If you and your girlfriend both have access to computers with Internet connections you can play online multiplayer games together while talking on the phone. There are a wide variety of free multiplayer gaming websites. In order to connect directly to one another you'll likely need to create an account. Multiplayer computer games include word games, board games, racing games and roll playing games. Choose something you both have an interest in.
20 Questions
A game of 20 Questions is easily playable on the phone and tests your memory of certain areas. This game is best played while you are both in rooms that the other one has been in frequently. One person takes a turn coming up with an object within their site. You ask questions about the object while picturing the room in your head as best as possible. Questions can only have a yes or no answer. Try your best to guess the object within 20 questions.