If users of your application are frustrated that they constantly have to log in to Facebook, or if it's inconvenient for your application to incessantly prompt the user to log in to Facebook, we hope that this functionality will be useful. You may notice that there's a new "Save my login info" checkbox on the Facebook application login page.
To take advantage of infinite sessions, your application should permanently store a user's session key and include it in method calls. You won't ever need to establish a new session on behalf of that user, unless the user explicitly logs out of your application. To see infinite sessions in action, check out the Facebook Exporter for iPhoto - once logged in to Facebook for the first time, users should never have to log in again.
As always, we respect the privacy of our users, and that's why we require users to enter their passwords when establishing an infinite session. Users can log out of any application (for which a session has been established) on the newly redesigned privacy page.
To learn more about infinite sessions (including how to obtain one), check out the updated authentication guide.