What is the maximum pitch for the Boeing 787 Dreamliner?
30 degrees.

Boeing aircraft, including the 787, have a Pitch Limit Indicator (PLI) in the flight display that tells the pilot how far the wing's angle of attack (AOA) is from stall.




  the PLI also is limited to 30 deg of pitch attitude, regardless of AOA.


But it depends on aircraft configuration


  During takeoff climb, there is no single target AOA to fly that will guarantee certified takeoff performance. Takeoff-climb AOA will vary with such factors as airplane gross weight, thrust, altitude, flap setting, and CG. Takeoff-climb speeds (hence, AOA) are limited by stall speed, tail clearance, and minimum control speeds. The higher speed and greater thrust of an all-engine takeoff reduce the AOA significantly relative to an engine-out takeoff at the engine-out climb speed (V2 ).


From Boeing Aero No.12



At Farnborough 2014, pilots Neville and Bryan were pulling stunts that would get airline pilots fired. Most airlines limit pitch to 20 degrees (or in a few cases 25) from what I've read.


  They kicked off the demonstration with a spectacularly steep takeoff, pitching the plane up just shy of 30 degrees. 


I'd guess they flew just inside what Boeing consider unsafe for those conditions.


  Boeing won’t reveal ... just how steeply it can take off


From Wired - "terrifying" (my emphasis). 

I think we can be reasonably confident that no production 787 will ever, after take-off, initially climb at greater than 30 degrees.



Flight envelopes

The way I understand it, asking about the "maximum" of anything for an aircraft is less useful than understanding the flight envelope. This is because the maximum depends very greatly on the exact situation of the aircraft including things like altitude, weight, speed etc.


Actual flight data from the six Boeing 787 test aircraft.