Genome-wide sequencing in a research setting has the potential to reveal health-related information of personal or clinical utility for the study participant. There is increasing pressure to return research findings to participants that may not be related to the project aims, particularly when these could be used to prevent disease. Such secondary, unsolicited or 'incidental findings' (IFs) may be discovered unintentionally when interpreting sequence data, or as the result of a deliberate opportunistic screen. This cross-sectional, web-based survey investigated attitudes of 6944 individuals from 75 countries towards returning IFs from genome research. Participants included four relevant stakeholder groups: 4961 members of the public, 533 genetic health professionals, 843 non-genetic health professionals and 607 genomic researchers who were invited via traditional media, social media and professional e-mail list-serve. Treatability and perceived utility of incidental results were deemed important with 98% of stakeholders personally interested in learning about preventable life-threatening conditions. Although there was a generic interest in receiving genomic information, stakeholders did not expect researchers to opportunistically screen for IFs in a research setting. On many items, genetic health professionals had significantly more conservative views compared with other stakeholders. This finding demonstrates a disconnect between the views of those handling the findings of research and those participating in research. Exploring, evaluating and ultimately addressing this disconnect should form a priority for researchers and clinicians alike. This social sciences study offers the largest dataset, published to date, of attitudes towards issues surrounding the return of IFs from sequencing research.