Brain-Computer Interface (BCI) is a system empowering humans to communicate with or control the outside world with exclusively brain intentions. Electroencephalography (EEG) based BCIs are promising solutions due to their convenient and portable instruments. Despite the extensive research of EEG in recent years, it is still challenging to interpret EEG signals effectively due to the massive noises in EEG signals (e.g., low signal-noise ratio and incomplete EEG signals), and difficulties in capturing the inconspicuous relationships between EEG signals and certain brain activities. Most existing works either only consider EEG as chain-like sequences neglecting complex dependencies between adjacent signals or requiring preprocessing such as transforming EEG waves into images. In this paper, we introduce both cascade and parallel convolutional recurrent neural network models for precisely identifying human intended movements and instructions by effectively learning the compositional spatio-temporal representations of raw EEG streams. Extensive experiments on a large scale movement intention EEG dataset (108 subjects, 3,145,160 EEG records) have demonstrated that both models achieve high accuracy near 98.3% and outperform a set of baseline methods and most recent deep learning based EEG recognition models, yielding a significant accuracy increase of 18% in the cross-subject validation scenario. The developed models are further evaluated with a real-world BCI and achieve a recognition accuracy of 93% over five instruction intentions. This suggests the proposed models are able to generalize over different kinds of intentions and BCI systems.