Many of the most popular applications, or "apps," on the social-networking site Facebook Inc. have been transmitting identifying information—in effect, providing access to people's names and, in some cases, their friends' names—to dozens of advertising and Internet tracking companies, a Wall Street Journal investigation has found.

The issue affects tens of millions of Facebook app users, including people who set their profiles to Facebook's strictest privacy settings. The practice breaks Facebook's rules, and renews...