This paper presents a framework and an initial study in general video game level generation, the problem of generating levels for not only a single game but for any game within a specified range. While existing level generators are tailored to a particular game, this new challenge requires generators to take into account the constraints and affordances of games that might not even have been designed when the generator was constructed. The framework presented here builds on the General Video Game AI framework (GVG-AI) and the Video Game Description Language (VGDL), in order to reap synergies from research activities connected to the General Video Game Playing Competition. The framework will also form the basis for a new track of this competition. In addition to the framework, the paper presents three general level generators and an empirical comparison of their qualities.