Microsoft says that they're working on fixing the issue, they'll have an update for users at around 1:20 PM Eastern. Assuming you can sign in, there appear to be no issues with purchasing and using content or social and gaming functions.
We'll update this post when full service is restored. You can check Xbox Live's status on the status page for more info.
Update: And it looks like the issue has been fixed, as of 1:36 PM Eastern, and users should have no trouble signing into Xbox Live.