When combined with In-Context Learning, a technique that enables models to adapt to new tasks by incorporating task-specific examples or demonstrations directly within the input prompt, autoregressive language models have achieved good performance in a wide range of tasks and applications. However, this combination has not been properly explored in the context of named entity recognition, where the structure of this task poses unique challenges. We propose RENER (Retrieval-Enhanced Named Entity Recognition), a technique for named entity recognition using autoregressive language models based on In-Context Learning and information retrieval techniques. When presented with an input text, RENER fetches similar examples from a dataset of training examples that are used to enhance a language model to recognize named entities from this input text. RENER is modular and independent of the underlying language model and information retrieval algorithms. Experimental results show that in the CrossNER collection we achieve state-of-the-art performance with the proposed technique and that information retrieval can increase the F-score by up to 11 percentage points.