Both research and commercial machine translation have so far neglected the importance of properly handling the spelling, lexical and grammar divergences occurring among language varieties. Notable cases are standard national varieties such as Brazilian and European Portuguese, and Canadian and European French, which popular online machine translation services are not keeping distinct. We show that an evident side effect of modeling such varieties as unique classes is the generation of inconsistent translations. In this work, we investigate the problem of training neural machine translation from English to specific pairs of language varieties, assuming both labeled and unlabeled parallel texts, and low-resource conditions. We report experiments from English to two pairs of dialects, European-Brazilian Portuguese and European-Canadian French, and two pairs of standardized varieties, Croatian-Serbian and Indonesian-Malay. We show significant BLEU score improvements over baseline systems when translation into similar languages is learned as a multilingual task with shared representations.