Dialog state tracking is a key component of many modern dialog systems, most of which are designed with a single, well-defined domain in mind. This paper shows that dialog data drawn from different dialog domains can be used to train a general belief tracking model which can operate across all of these domains, exhibiting superior performance to each of the domain-specific models. We propose a training procedure which uses out-of-domain data to initialise belief tracking models for entirely new domains. This procedure leads to improvements in belief tracking performance regardless of the amount of in-domain data available for training the model.