What runway has the steepest climb requirement on take-off?
The first one that came to mind is London City Airport (EGLC) which is world famous for its steep approaches, and for which I found these requirements on its departure charts:


  OBSTACLE CLEARANCE -
  RWY 09: Maintain minimum 6.76% climb gradient to 275 (258).
  RWY 27: Maintain minimum 7.20% climb gradient to 1102 (1085).


(Where the first number is altitude in feet and the second number is AAL, above aerodrome level)