Facebook’s standard app login (i.e. apps other than Facebook) will allow users to control which parts of your profile is available. The whole point of using Facebook login is that it keeps you from making yet another account, but Facebook contains so much more data than you’d usually give to some random app developer.
This update to the Facebook platform lets you close off just about all parts of your profile to an app. The only required item is your public profile, which is how the app identifies you. Of course, you are also free to just hit the accept button and let the app use the defaults. Additionally, apps will need explicit permission to post to your feed now.
The anonymous login option is a bit more interesting. If you choose to go this route, the app gets no data about you at all, but you can still use it normally (minus any social features that would necessitate access to your profile). After getting to know an app, you can switch from anonymous logins to the standard version to get all the social features and share information with the app.
The new login will be rolling out in apps over the next few months, but the anonymous version is still being tested by a limited number of developers. It will be made available to everyone later this year.