Trust may be important in shaping public attitudes to genetics and intentions to participate in genomics research and big data initiatives. As such, we examined trust in data sharing among the general public. A cross-sectional online survey collected responses from representative publics in the USA, Canada, UK and Australia (n = 8967). Participants were most likely to trust their medical doctor and less likely to trust other entities named. Company researchers were least likely to be trusted. Low, Variable and High Trust classes were defined using latent class analysis. Members of the High Trust class were more likely to be under 50 years, male, with children, hold religious beliefs, have personal experience of genetics and be from the USA. They were most likely to be willing to donate their genomic and health data for clinical and research uses. The Low Trust class were less reassured than other respondents by laws preventing exploitation of donated information. Variation in trust, its relation to areas of concern about the use of genomic data and potential of legislation are considered. These findings have relevance for efforts to expand genomic medicine and data sharing beyond those with personal experience of genetics or research participants.