Neural parsers obtain state-of-the-art results on benchmark treebanks for constituency parsing—but to what degree do they generalize to other domains? We present three results about the generalization of neural parsers in a zero-shot setting: training on trees from one corpus and evaluating on out-of-domain corpora. First, neural and non-neural parsers generalize comparably to new domains. Second, incorporating pre-trained encoder representations into neural parsers substantially improves their performance across all domains, but does not give a larger relative improvement for out-of-domain treebanks. Finally, despite the rich input representations they learn, neural parsers still benefit from structured output prediction of output trees, yielding higher exact match accuracy and stronger generalization both to larger text spans and to out-of-domain corpora. We analyze generalization on English and Chinese corpora, and in the process obtain state-of-the-art parsing results for the Brown, Genia, and English Web treebanks.