If Twitter suddenly logged you out of your mobile apps and won't let you back in — or a device or a desktop, actually — you're not alone. In fact, you're in damned good company. We're locked out, too. Twitter's official status page says they're aware of the problem and are working on it.
One possible culprit, as noted in our comments, is that apparently Twitter leaped ahead to Dec 29, 2015. While we have no doubt that day will be awesome, it's still a year away and unsurprisingly would cause issues should servers think we're there already.
Update: Here's a possible culprit:
I MITMed Twitter for Android's login to see why it was failing. The Twitter servers think it's 2015. Amazing. pic.twitter.com/iEu4rEUub9— Ninji the [REDACTED] (@_Ninji) December 29, 2014
Update 2: Twitter is on it
Update 3: The issue has been resolved:
The issue that prevented some users from signing in to Twitter has been resolved. We apologize for the inconvenience: http://t.co/7BlGvFMC3e— Twitter Support (@Support) December 29, 2014