Is a player allowed to count the number of cards in his/her deck during a game, provided he/she doesn't change the order of the cards? And if so, is it permissible to count your opponent's deck as well?
Yes, the number of cards in both your and your opponent's deck are public information. Although it is recommended that the player counts his or her cards during their opponent's turn, in a manner that doesn't disrupt or slow down the game.
Source: PUI Rules Team (2004-05-06)