Probabilistic forecasting that quantifies the prediction uncertainties is crucial for decision-making in power systems. As a prevalent nonparametric probabilistic forecasting approach, traditional machine learning-based quantile regression encounters the quantile crossing problem. This paper proposes a novel ensemble deep learning based non-crossing quantile regression (EDNQR) model for probabilistic wind power forecasting, which does not need any distribution assumption and demonstrates high generalization ability. A unique non-crossing quantile regression strategy is proposed to generate monotonous quantiles with deep learning models. The exponential stacking mapping method is proposed to guarantee the monotonicity of quantiles, and Huber norm pinball loss is introduced for deep learning quantile regression model training. To improve the generalization capability, a two-stage ensemble framework is proposed to integrate homogeneous and heterogeneous deep learning models. The newly-trained base model considers the training performance of the last base model, which benefits the performance boosting of the ensemble model. To overcome the complexity of conventional weight optimization-based model integration, an overall quantile loss index is proposed to serve as an indicator to directly integrate both the homogeneous and heterogeneous deep learning base models. Comprehensive numerical studies based on actual wind farm data validate the superior performance of the proposed EDNQR model in terms of reliability, overall skill and generalization ability.