Just as the folks at Sony preview the future with their latest State of Play event, Xbox players are unable to login at all, as the online service is suffering a major outage. The latest update from 5 PM ET indicates Microsoft is working on the issue, but doesn't provide any kind of ETA for when it will be resolved. According to the Xbox Live Status page, the outage started around 3:15 PM ET, and there's no sign yet of anything getting better.
Update: As of 5:10 PM ET the status page's latest update says "we're close to resolving the issue," so hang in there.
Update 2: 15 minutes later, and the status is still "close" so hopefully playing offline (head to the network settings and select "go offline") is working for you, otherwise even single player games are out of the question for now.
Update 3 (6 PM ET): It's been nearly three hours, and while the status still says a resolution is close, everything is still offline.
Update 4 (8 PM ET): Nearly five hours after the outage began and it's still going, meanwhile the status page has updated its message to say "It's taking longer than anticipated."
Update 5 (9 PM ET): The message has been updated again to note a resolution is close, and many reports on social media show players are able to login again after restarting their systems.
Update 6 (9:36 PM ET): The status page shows "all clear" and people seem to be able to play again, if you're still not connecting try restarting first.