How many aircraft types are cabin crew qualified for?
I know very little about this, but in the US the regulations appear to say that cabin crew must be qualified by aircraft type and the details are part of the approved training program for each operator (airline).

In the US, 14 CFR Part 121 governs airline operations, and 121.392 says:


  (a) Any person identified by the certificate holder as a flight
  attendant on an aircraft in operations under this part must be trained
  and qualified in accordance with subparts N and O of this part.


Subparts N and O are far too long to quote here (you can always read them yourself), but 121.421 is probably the most relevant regulation to what you're asking:


  §121.421   Flight attendants: Initial and transition ground training.
  
  (a) Initial and transition ground training for flight attendants must
  include instruction in at least the following:
  
  (1) General subjects—
  
  (i) The authority of the pilot in command;
  
  (ii) Passenger handling, including the procedures to be followed in
  the case of deranged persons or other persons whose conduct might
  jeopardize safety; and
  
  (iii) Approved crew resource management initial training.
  
  (2) For each airplane type—
  
  (i) A general description of the airplane emphasizing physical
  characteristics that may have a bearing on ditching, evacuation, and
  inflight emergency procedures and on other related duties;
  
  (ii) The use of both the public address system and the means of
  communicating with other flight crewmembers, including emergency means
  in the case of attempted hijacking or other unusual situations; and
  
  (iii) Proper use of electrical galley equipment and the controls for
  cabin heat and ventilation.
  
  (b) Initial and transition ground training for flight attendants must
  include a competence check to determine ability to perform assigned
  duties and responsibilities.
  
  [...]


I couldn't see any limitation on the number of "airplane types" that a flight attendant can be qualified in, but the training is administered by the airline so if there is a limitation it may set by them rather than by the FAA. 121.427 requires recurrent training (but it doesn't say how often) and I assume that at some point a flight attendant who's qualified on multiple aircraft types could end up spending more time training than actually working on flights. That's unlikely to be something that the airline wants to happen.