In this paper, we study the problem of enabling neural machine translation (NMT) to reuse previous translations from similar examples in target prediction. Distinguishing reusable translations from noisy segments and learning to reuse them in NMT are non-trivial. To solve these challenges, we propose an Example-Guided NMT (EGNMT) framework with two models: (1) a noise-masked encoder model that masks out noisy words according to word alignments and encodes the noise-masked sentences with an additional example encoder and (2) an auxiliary decoder model that predicts reusable words via an auxiliary decoder sharing parameters with the primary decoder. We define and implement the two models with the state-of-the-art Transformer. Experiments show that the noisemasked encoder model allows NMT to learn useful information from examples with low fuzzy match scores (FMS) while the auxiliary decoder model is good for high-FMS examples. More experiments on Chinese-English, English-German and English-Spanish translation demonstrate that the combination of the two EGNMT models can achieve improvements of up to +9 BLEU points over the baseline system and +7 BLEU points over a two-encoder Transformer.