Serious games have become a key segment in the games market as well as in academic research. Although the number of games that identify themselves as belonging to this category as well as the research done on their effects has been rapidly growing, there has thus far been no attempt to define all of the various opportunities that digital games provide for learning. To address this issue we look at existing definitions of serious games and their potential for learning. We identify the shortcomings of existing definitions and typologies. We discuss opportunities for an educational use of serious games which have been marginalized so far and develop a more flexible classification system for serious games in order to include commercial-off-the-shelf (COTS) games for learning purposes and description options for future developments of gaming technology. This classification system for digital and serious games uses labels and tags as a preferable solution instead of fixed genre categories. The aim of this paper is to move the focus from what serious games and their uses for learning currently are to what they can be.