It's not clear exactly what prompted the breakdown, but the company's Brad Rossetti has confirmed that a "service change" was responsible. It's rolling things back, he said. There was no estimated time for when consoles would return to a healthy state, but they could be fine by the time you read this.
Whatever the cause, the incident highlights one of the potential problems with deeply integrated online features in consoles -- they can render the machines unusable in the wrong circumstances. It's safe to say Microsoft will want to learn lessons from this mess, especially if rumors of a cloud-only Xbox are true.
Update 1/30 3:35PM ET: Microsoft has resolved the various problems (we've verified this with one of our consoles). There's no detailed explanation yet, but it's now safe to pick up your controller and start playing.