Previous work has suggested that parameter sharing between transition-based neural dependency parsers for related languages can lead to better performance, but there is no consensus on what parameters to share. We present an evaluation of 27 different parameter sharing strategies across 10 languages, representing five pairs of related languages, each pair from a different language family. We find that sharing transition classifier parameters always helps, whereas the usefulness of sharing word and/or character LSTM parameters varies. Based on this result, we propose an architecture where the transition classifier is shared, and the sharing of word and character parameters is controlled by a parameter that can be tuned on validation data. This model is linguistically motivated and obtains significant improvements over a monolingually trained baseline. We also find that sharing transition classifier parameters helps when training a parser on unrelated language pairs, but we find that, in the case of unrelated languages, sharing too many parameters does not help.