Most modern Information Extraction (IE) systems are implemented as sequential taggers and only model local dependencies. Non-local and non-sequential context is, however, a valuable source of information to improve predictions. In this paper, we introduce GraphIE, a framework that operates over a graph representing a broad set of dependencies between textual units (i.e. words or sentences). The algorithm propagates information between connected nodes through graph convolutions, generating a richer representation that can be exploited to improve word-level predictions. Evaluation on three different tasks — namely textual, social media and visual information extraction — shows that GraphIE consistently outperforms the state-of-the-art sequence tagging model by a significant margin.