Transcription activator-like effector (TALE) proteins recognize DNA using a seemingly simple DNA-binding code, which makes them attractive for use in genome engineering technologies that require precise targeting. Although this code is used successfully to design TALEs to target specific sequences, off-target binding has been observed and is difficult to predict. Here we explore TALE-DNA interactions comprehensively by quantitatively assaying the DNA-binding specificities of 21 representative TALEs to ∼5,000-20,000 unique DNA sequences per protein using custom-designed protein-binding microarrays (PBMs). We find that protein context features exert significant influences on binding. Thus, the canonical recognition code does not fully capture the complexity of TALE-DNA binding. We used the PBM data to develop a computational model, Specificity Inference For TAL-Effector Design (SIFTED), to predict the DNA-binding specificity of any TALE. We provide SIFTED as a publicly available web tool that predicts potential genomic off-target sites for improved TALE design.