How long is a climb leg in a step-climb cruise flight segment allowed to take, according to regulations (FAA/EASA)?
The FAA's IFR handbook sheds some light on what they expect (page 2-48) 


  If the pilot receives the term “climb at pilot’s discretion” in the
  altitude information of an ATC clearance, it means that the pilot has
  the option to start a climb when they desire and are authorized to
  climb at any rate, and to temporarily level off at any intermediate
  altitude as desired, although once you vacate an altitude, you may not
  return to that altitude. When ATC has not used the term nor imposed
  any climb restrictions, pilots should climb promptly on acknowledgment
  of the clearance. Climb at an optimum rate consistent with the
  operating characteristics of the aircraft to 1,000 feet below the
  assigned altitude, and then attempt to climb at a rate of between 500
  and 1,500 fpm until the assigned altitude is reached.


Its somewhat contradictory, first they say you can climb at any rate you want but then they say in the absence of any specific instructions you should climb at an "optimum" rate to within 1000 feet of your assigned altitude and then climb between 500fpm and 1500fpm. 

This is specifically spelled out in the AIM with more or less the same language 


  When ATC has not used the term “AT PILOT’S DISCRETION” nor imposed any
  climb or descent restrictions, pilots should initiate climb or
  descent promptly on acknowledgement of the clearance.Descend or climb
  at an optimum rate consistent with the operating characteristics of the
  aircraft to1,000 feet above or below the assigned altitude, and then
  attempt to descend or climb at a rate of between 500 and 1,500 fpm
  until the assigned altitude is reached. If at anytime the pilot is
  unable to climb or descend at a rate of at least 500 feet a minute,
  advise ATC.


Interestingly this adds the note that if you can not climb at 500 f/min then you should alert ATC. I would take this to be a minimum climb rate. 

There is at least one permitted case of the drift climb that I know of. The Concorde operated above all other commercial traffic and aside from the SR-71 there really was no one else up where they were. As such once they passed a specific floor they were allowed to drift up freely as they burned fuel. This was, as far as I know unique to their operation and specifically permitted. They had a lot of other specific addendums due to their unique design.