Neural methods have been shown to achieve high performance in Named Entity Recognition (NER), but rely on costly high-quality labeled data for training, which is not always available across languages. While previous works have shown that unlabeled data in a target language can be used to improve cross-lingual model performance, we propose a novel adversarial approach (AdvPicker) to better leverage such data and further improve results. We design an adversarial learning framework in which an encoder learns entity domain knowledge from labeled source-language data and better shared features are captured via adversarial training - where a discriminator selects less language-dependent target-language data via similarity to the source language. Experimental results on standard benchmark datasets well demonstrate that the proposed method benefits strongly from this data selection process and outperforms existing state-of-the-art methods; without requiring any additional external resources (e.g., gazetteers or via machine translation).