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One of the grand challenges of AI is to create general intelligence: an agent that can excel at many tasks, not just one. In the area of games, this has given rise to the challenge of General Game Playing (GGP). In GGP, the game (typically a turn-taking board game) is defined declaratively in terms of the logic of the game (what happens when a move is made, how the scoring system works, how the winner is declared, and so on). The AI player then has to work out how to play the game and how to win. In this work, we seek to extend the idea of General Game Playing into the realm of video games, thus forming the area of General Video Game Playing (GVGP). In GVGP, computational agents will be asked to play video games that they have not seen before. At the minimum, the agent will be given the current state of the world and told what actions are applicable. Every game tick the agent will have to decide on its action, and the state will be updated, taking into account the actions of the other agents in the game and the game physics. We envisage running a competition based on GVGP playing, using arcadestyle (e.g. similar to Atari 2600) games as our starting point. These games are rich enough to be a formidable challenge to a GVGP agent, without introducing unnecessary complexity. The competition that we envisage could have a number of tracks, based on the form of the state (frame buffer or object model) and whether or not a forward model of action execution is available. We propose that the existing Physical Travelling Salesman (PTSP) software could be extended for our purposes and that a variety of GVGP games could be created in this framework by AI and Games students and other developers. Beyond this, we envisage the development of a Video Game Description Language (VGDL) as a way of concisely specifying video games. For the competition, we see this as being an interesting challenge in terms of deliberative search, machine learning and transfer of existing knowledge into new domains.