There are also significant benefits to biological research. Most genetic variation is rare, and the effect of each of these rare variants is small, but they add up. Having access to larger datasets will allow us to be able to better correlate those variants to diseases. 23andme is already doing this with Genentech: http://www.forbes.com/sites/matthewherper/2015/01/06/surpris....
But what if 23andme or Genentech starts selling people's data to health and life insurance firms? And maybe employers will want that data, just as they want credit reports etc.
There ought to be meaningful privacy protection, in my opinion.
Not life insurance firms, yet, though.
See for example http://www.ncbi.nlm.nih.gov/pubmed/23329047
23andme knows my DNA. They know my email, and possibly where I bought the kit.
They don't know who I am, I hope.
And, regardless, I suspect the de-anonymization will be either so haphazard or so thorough in the future that it's not a primary concern.
Bottom line, I see no compelling upside to putting ones DNA data on the Internet.