What is the maximum slope for taxiing aircraft?
Footnote: I hope this is the correct/ current regulation. Published date is 25 January 2015.

Your question is covered (for EASA regulations) in the document Certification Specifications and Guidance Material for Aerodromes Design (link) in two sections: 


Taxiway Slope (CS ADR-DSN.D.265)
Taxiway Slope changes (CS ADR-DSN.D.270)



  CS ADR-DSN.D.265 Longitudinal slopes on taxiways 
  
  (a) The safety objective of limiting the longitudinal taxiway slope
  is to enable stabilised safe use of taxiway by an aircraft.
  
  (b) The longitudinal slope of a taxiway should not exceed:
  
  
  1.5% where the code letter is C, D, E, or F; and
  3% where the code letter is A or B.
  
  
  CS ADR-DSN.D.270 Longitudinal slope changes on taxiways
  
  (a) The safety objective of limiting the longitudinal taxiway slope
  changes is to avoid damage of aircraft and to enable safe use of
  taxiway by an aircraft.
  
  (b) Where slope changes on a taxiway cannot be avoided, the transition
  from one slope to another slope should be accomplished by a curved
  surface with a rate of change not exceeding:
  
  
  1% per 30m (minimum radius of curvature of 3000m) where the code letter is C, D, E,or F; and
  1% per 25m (minimum radius of curvature of 2500m) where the code letter is A or B.
  
  
  (c) Where slope changes in (b)(1) and (2)  are not  achieved and
  slopes on a taxiway cannot  be avoided, the  transition  from  one 
  slope  to  another  slope  should  be  accomplished  by  a  curved 
  surface  which  should allow the safe operation of all aircraft in all
  weather conditions.


The letters refer to the airport categorization.