Informal social interaction is the primordial home of human language. Linguistically diverse conversational corpora are an important and largely untapped resource for computational linguistics and language technology. Through the efforts of a worldwide language documentation movement, such corpora are increasingly becoming available. We show how interactional data from 63 languages (26 families) harbours insights about turn-taking, timing, sequential structure and social action, with implications for language technology, natural language understanding, and the design of conversational interfaces. Harnessing linguistically diverse conversational corpora will provide the empirical foundations for flexible, localizable, humane language technologies of the future.