The ability to effectively classify electroencephalograms (EEG) is the foundation for building usable Brain-Computer Interfaces as well as improving the performance of EEG analysis software used in clinical and research settings. Although a number of research groups have demonstrated the feasibility of EEG classification, these methods have not yet reached a level of performance that is acceptable for use in many practical applications. We assert that current approaches are limited by their ability to capture the temporal and spatial patterns contained within EEG. In order to address these problems, we propose a new generative technique for EEG classification that uses Elman Recurrent Neural Networks. EEG recorded while a subject performs one of several imagined mental tasks is first modeled by training a network to forecast the signal a single step ahead in time. We show that these models are able to forecast EEG with an error as low as 1.18 percent of the signal range. A separate model is then trained over EEG belonging to each class. Classification of previously unseen data is performed by applying each model and using Winner-Takes-All, Linear Discriminant Analysis or Quadratic Discriminant Analysis to label the forecasting errors. This approach is tested on EEG collected from two able-bodied subjects and three subjects with disabilities. Information transfer rates as high as 38.7 bits per minute (bpm) are achieved for a two-task problem and 34.5bpm for a four-task problem.