Open-domain conversational systems are assumed to generate equally good responses on multiple domains. Previous work achieved good performance on the single corpus, but training and evaluating on multiple corpora from different domains are less studied. This paper explores methods of generating relevant responses for each of multiple multi-domain corpora. We first examine interleaved learning which intermingles multiple corpora as the baseline. We then investigate two multi-domain learning methods, labeled learning and multi-task labeled learning, which encode each corpus through a unique corpus embedding. Furthermore, we propose Domain-specific Frequency (DF), a novel word-level importance weight that measures the relative importance of a word for a specific corpus compared to other corpora. Based on DF, we propose weighted learning, a method that integrates DF to the loss function. We also adopt DF as a new evaluation metric. Extensive experiments show that our methods gain significant improvements on both automatic and human evaluation. We share our code and data for reproducibility.