People increasingly turn to the Internet when they have a medical condition. The data they create during this process is a valuable source for medical research and for future health services. However, utilizing these data could come at a cost to user privacy. Thus, it is important to balance the perceived value that users assign to these data with the value of the services derived from them. Here we describe experiments where methods from Mechanism Design were used to elicit a truthful valuation from users for their Internet data and for services to screen people for medical conditions. In these experiments, 880 people from around the world were asked to participate in an auction to provide their data for uses differing in their contribution to the participant, to society, and in the disease they addressed. Some users were offered monetary compensation for their participation, while others were asked to pay to participate. Our findings show that 99\% of people were willing to contribute their data in exchange for monetary compensation and an analysis of their data, while 53\% were willing to pay to have their data analyzed. The average perceived value users assigned to their data was estimated at US\$49. Their value to screen them for a specific cancer was US\$22 while the value of this service offered to the general public was US\$22. Participants requested higher compensation when notified that their data would be used to analyze a more severe condition. They were willing to pay more to have their data analyzed when the condition was more severe, when they had higher education or if they had recently experienced a serious medical condition.