PSA: Xbox Live sign-in issues ongoing, Microsoft working on them [update]
Folks trying to sign into Xbox Live right now may encounter some issues, specifically that they, well, can't. Microsoft is aware of the situation, however, and is working to resolve it. No ETA has been given for a fix, so we recommend doing what we always do whenever there's some sort of ongoing service outage: Watch Girls' Generation videos on YouTube and wait for everything to blow over.
Update: Limited connectivity appears to have returned, although Microsoft warns that users may still encounter errors while managing their friends lists and/or while attempting to send text or voice messages over Xbox Live.
[Thanks to everyone who sent this in!]