UPDATE: Thankfully, after just three days in emergency mode, NASA engineers have managed to stabilize the Kepler spacecraft. It will resume its observations, despite the cause of the original emergency remaining unclear.
Mission engineers have declared a spacecraft emergency after scheduled contact with the Kepler spacecraft revealed it had gone into emergency mode. Analogous to a computer's safe mode, the Kepler spacecraft's emergency mode causes it to cease observing and obtain a position best for communication, which is difficult given Kepler is 75 million miles from Earth. This results in a delay in communications of about 13 minutes. Emergency mode is the lowest operational mode and, unfortunately, means Kepler is also using more fuel than planned due to the previous loss of its two primary reaction wheels (2012 and 2013). I will be updating the Storify version of this article with key components of the ongoing Twitter conversation!
The cause of the spacecraft emergency is not known at this time, though the fact contact has been established is a good sign. The emergency was discovered when NASA engineers attempted to point the spacecraft towards the center of the Milky Way in order to begin the K2 microlensing observing campaign.
The K2 microlensing observing campaign is a mission to detect exoplanets (planets around stars other than the Sun) that are far from their host stars. Currently, the most popular methods of detecting exoplanets favor larger planets closer to their host stars. In contrast, this observing campaign plans to search for the sudden brightening of starlight caused by a planet passing between a distant star and the Kepler spacecraft. The gravitational force of the planet acts like a lens (a "microlens"), magnifying and concentrating the starlight. This allows astronomers to detect planets at distances previously thought impossible. The same process yields stunning "Einstein rings", though the lens in this case is much larger (a galaxy vs a planet). Hopefully, Kepler's emergency mode was triggered by something innocuous and recovery will be easy - unlike the emergency faced by JAXA's Hitomi (ASTRO-H) x-ray satellite.