Multi-head attention has each of the attention heads collect salient information from different parts of an input sequence, making it a powerful mechanism for sequence modeling. Multilingual and multi-domain learning are common scenarios for sequence modeling, where the key challenge is to maximize positive transfer and mitigate negative interference across languages and domains. In this paper, we find that non-selective attention sharing is sub-optimal for achieving good generalization across all languages and domains. We further propose attention sharing strategies to facilitate parameter sharing and specialization in multilingual and multi-domain sequence modeling. Our approach automatically learns shared and specialized attention heads for different languages and domains. Evaluated in various tasks including speech recognition, text-to-text and speech-to-text translation, the proposed attention sharing strategies consistently bring gains to sequence models built upon multi-head attention. For speech-to-text translation, our approach yields an average of $+2.0$ BLEU over $13$ language directions in multilingual setting and $+2.0$ BLEU over $3$ domains in multi-domain setting.