Web measurement firm Compete has provided us with a closer look at the traffic Facebook received from other web sites in May. The data, which is broken down by category and by individual site, shows increases in referrals from entertainment sites, with small drops from email providers and other social networking services. Direct and search are the biggest sources of Facebook traffic, and those stayed roughly flat.

Overall, Compete showed Facebook growing by 2.1 million new US users in May to reach 123.8 million monthly unique visitors. This is roughly in line with other measurement firms, and indicates that Facebook grew despite the very public privacy controversies that unfolded over the month. See our post from earlier this week for more details on that topic.

Note that Compete’s “Channel Map” data visualization shows categories by share, not absolute numbers; the traffic details section, however, does show absolute numbers. You can check it out here.

The categories growing their shares the most, according to Compete, included music and videos, gaming, hobbies and interests, television and movie guide sites and sports. Many individual entertainment-focused sites integrated the Like Button and other social plugins in May, which could help explain the increases.

Overall, the site that sent by far the most new traffic to Facebook was Yahoo, including its many content subdomains: it contributed 293 million referrals in May, with an increase of 28.5 million. One reason for this growth might be Yahoo’s ongoing integrations of Facebook features — although much of what it’s planning has only just rolled out, or is not yet available.

The single biggest drop came in traffic from another social network — MySpace. That site sent a total of 67.6 million referrals to Facebook in May, the third largest after Google and Yahoo. But it feel by 1.86 million versus last month. Microsoft’s Live.com fell even more, down to 2.79 million to 54.8 million referrals. Dropping categories included dating (due to a massive, strange fall from Match.com), colleges and universities (school just got out) and email (no wonder Facebook executives have little enthusiasm for email).