What is the backup for a glass cockpit, if a plane loses power to the displays/controls?
I'll answer this question as "If the glass cockpit instrument fail, what are the backup? " This answer will also be General Aviation oriented (as I'm a PPL student) 

The short answer is redundancy. 

At first, let's look at a G1000 (standard GA glass cockpit) architecture : 


The most important components are : 


One (or multiple for redundancy) AHRS : gives information about Attitude and Heading of the aircraft, thanks to electronic gyrometres / accelerometres / magnetometres. 
One (or multiple) Air Data Computer: gives information regarding airspeed / vertical speed / altitude, thanks to static / dynamic pressure informations. 
And two Integrated Avionics Unit, that collect data from AHRS / ADC, and generate the content displayed on screen.


Now, Although the two screens usually don't display the same informations (PFD and MFD), These two systems are standalone : in case of a screen / Avionic unit failure, the second can take other.

Here the goal is to remove all single points of failure. 


  But what if the whole EFIS fails ?


It is required by law to have backup of essential instruments. The definition of "essential" depends of the type of flight (day VFR, night VFR or IFR?). For some aircraft, there backups are traditional (steam gauge) instruments / others have independent electronic systems, like the new Cirrus SR22 G6 : 


all electric !


  And in the case of a complete electrical failure? 


Depends of the aircraft. In my case, I fly the Robin DR401 (certified for night VFR):



The EFIS is a Garmin G500 (smaller version of G1000) along with a GTN650 GPS.

With such a cockpit, even if I have a complete loss of electrical power, backup instuments would still work : 


Altitude, Airspeed and Vertical Speed indicator don't require any power to operate ;
So does the slip/skid indicator (a simple ball)
And the Attitude indicator gyro is powered by a vacuum pump, linked to the engine ; it would thus still operate. 


In that case I'd be more concerned about the loss of radio / transponder / flaps control / trim than the loss of instruments!

To summarise, Glass Cockpits are designed to avoid the creation of single point of failure, to reduce the risk of complete loss of instruments, thanks to redundant system / backup instruments / displays... And for all-electric planes, I guess backup power supplies!