We report results from a large survey of public attitudes regarding genomic database governance. Prior surveys focused on the context of academic-sponsored biobanks, framing data provision as altruistic donation; our survey is designed to reflect four growing trends: genomic databases are found across many sectors; they are used for more than academic biomedical research; their value is reflected in corporate transactions; and additional related privacy risks are coming to light. To examine how attitudes may evolve in response to these trends, we provided survey respondents with information from mainstream media coverage of them. We then found only 11.7% of respondents willing to altruistically donate their data, versus 50.6% willing to provide data if financially compensated, and 37.8% unwilling to provide data regardless of compensation. Because providing one's genomic data is sometimes bundled with receipt of a personalized genomic report, we also asked respondents what price they would be willing to pay for a personalized report. Subtracting that response value from one's expected compensation for providing data (if any) yields a net expected payment. For the altruistic donors, median net expected payment was -$75 (i.e. they expected to pay $75 for the bundle). For respondents wanting compensation for their data, however, median net expected payment was +$95 (i.e. they expected to receive $95). When asked about different genomic database governance policies, most respondents preferred options that allowed them more control over their data. In particular, they favored policies restricting data sharing or reuse unless permission is specifically granted by the individual. Policy preferences were also relatively consistent regardless of the sector in which the genomic database was located. Together these findings offer a forward-looking window on individual preferences that can be useful for institutions of all types as they develop governance approaches in this area of large-scale data sharing.