Data augmentation is an important method for evaluating the robustness of and enhancing the diversity of training data for natural language processing (NLP) models. In this paper, we present NL-Augmenter, a new participatory Python-based natural language (NL) augmentation framework which supports the creation of transformations (modifications to the data) and filters (data splits according to specific features). We describe the framework and an initial set of 117 transformations and 23 filters for a variety of NL tasks annotated with noisy descriptive tags. The transformations incorporate noise, intentional and accidental human mistakes, socio-linguistic variation, semantically-valid style, syntax changes, as well as artificial constructs that are unambiguous to humans. We demonstrate the efficacy of NL-Augmenter by using its transformations to analyze the robustness of popular language models. We find different models to be differently challenged on different tasks, with quasi-systematic score decreases. The infrastructure, datacards, and robustness evaluation results are publicly available on GitHub for the benefit of researchers working on paraphrase generation, robustness analysis, and low-resource NLP.