In Catan, can I ask how many cards are in a player's hand?
Per the Settlers of Catan FAQ here:


  Is it true that the number of cards in your hand is always open and
  available information? Specifically, should it be readily apparent how
  many development cards you have, but have not yet played? Or can you
  hide the resource cards under the table or in your pocket so that no
  one can see how many cards you have?
  
  Yes. The quantity of cards you have in your hand is public
  information. But the identity of those cards is not. If another player
  asks, for example, how may resource cards do you have, right before he
  moves the robber, you must tell him truthfully the number of resource
  cards you have in your hand. The same goes for Development or Progress
  cards. The number of each type of card (resource, development, etc.)
  that you have is public knowledge at all times. (But, not the specific
  cards, i.e. wood, sheep, rock…)


It's a terrible idea to allow players to dissimulate about the number of cards in their hand.  For one thing, it means that unscrupulous types could pretend they didn't need to lose resources to the robber.  For another, it runs the risk of creating a situation where everyone has to keep track on paper or mentally of what everyone else draws just to make sensible plays, and that would be a big waste of time and effort.