We focus on improving name tagging for low-resource languages using annotations from related languages. Previous studies either directly project annotations from a source language to a target language using cross-lingual representations or use a shared encoder in a multitask network to transfer knowledge. These approaches inevitably introduce noise to the target language annotation due to mismatched source-target sentence structures. To effectively transfer the resources, we develop a new neural architecture that leverages multi-level adversarial transfer: (1) word-level adversarial training, which projects source language words into the same semantic space as those of the target language without using any parallel corpora or bilingual gazetteers, and (2) sentence-level adversarial training, which yields language-agnostic sequential features. Our neural architecture outperforms previous approaches on CoNLL data sets. Moreover, on 10 low-resource languages, our approach achieves up to 16% absolute F-score gain over all high-performing baselines on cross-lingual transfer without using any target-language resources.