We introduce a simple and accurate neural model for dependency-based semantic role labeling. Our model predicts predicate-argument dependencies relying on states of a bidirectional LSTM encoder. The semantic role labeler achieves competitive performance on English, even without any kind of syntactic information and only using local inference. However, when automatically predicted part-of-speech tags are provided as input, it substantially outperforms all previous local models and approaches the best reported results on the English CoNLL-2009 dataset. We also consider Chinese, Czech and Spanish where our approach also achieves competitive results. Syntactic parsers are unreliable on out-of-domain data, so standard (i.e., syntactically-informed) SRL models are hindered when tested in this setting. Our syntax-agnostic model appears more robust, resulting in the best reported results on standard out-of-domain test sets.