Bill,
With the huge influx of new players entering poker these days, the percentage of people who actually understand this rule has dropped off significantly - I'm glad you asked. Though anyone at the table can request to see a called hand, there is only one reason for this rule and that is so that each player can protect themselves against collusion. The rule is not in effect so that a player can learn how another player plays. If you think you were being whipsawed by a partnership for instance, that would be a valid reason for requesting to see a hand. If you can't imagine what he could possibly have to have called that huge raise but can't beat your busted straight draw on the end - that is not a valid reason.
In some of the very largest games if there is a request to see a hand the floorman is called. The floorman will ask how the betting went down and then look at the hand in question. If the betting sequence seems within reasonable parameters for the hand he is looking at he will simply muck the hand and it will not be shown. At the larger limits, typically the house charge is being paid by a time charge and so the house doesn't mind the delay of game - in the smaller games however, at $4 per hand, such a delay would cut into the casino's profits so we probably shouldn't hold our breathe waiting for this in those games.
In days past, asking to see someone's cards was the same as accusing them of cheating. I realize that most of todays newer players don't mean it that way - but I guess it's like an old time honorable businessman who's done all his business on a handshake and his word being told that he now needs to sign the contract... kind of insulting. I wouldn't worry too much about the newer players taking it that way but some of the old timers might stifle a desire to shove the cards somewhere.
TUP