At 1 a.m. on May 7, the website PatientsLikeMe.com noticed suspicious activity on its "Mood" discussion board. There, people exchange highly personal stories about their emotional disorders, ranging from bipolar disease to a desire to cut themselves.

It was a break-in. A new member of the site, using sophisticated software, was "scraping," or copying, every single message off PatientsLikeMe's private online forums.

PatientsLikeMe...