I've noticed in a few Poker apps that they show all the cards on a final checked or called round.
What is the law regarding mucking cards in this situation? This answer suggests everyone must show, is it correct ?
There are 2 main cases to the "who must show the cards" rule:
1). The last-aggressor situation.
This applies when there is some betting activity on the river. Let's take some examples:
Let's say there are 3 players playing (Small-Blind, Big-Blind and Under-the-Gun) and they got to the river.
When there is betting activity going on, the "who is first after the Dealer" order of acting is always in effect. Both the cases above overwrite this rule, as you can see (players in later positions end up acting first). This may feel "unnatural" at first, but you'll see that it makes sense and it's quite easy to get used to it.
(all the cases above are kind of the same, but I included them to show that both making a bet and making a raise will make you the last aggressor).
2). The check-check situation.
This applies when everyone checks on the river a.k.a. no betting activity (this is the situation you're most interested in, from what I can tell).
In this case, the first player left to the Dealer must show his cards. Going clockwise, subsequent players can each choose to show or muck, as they see fit.
Please note that these are the "official" rules. Each casino or home-game organizers can make up their own rules. However, you'll rarely see this, since it's pretty standard.
But you will see a lot of players or even dealers who often get it wrong. I see it all the time...
Upon showdown, all hands can be shown, which means that if player A asks to see player B's hand, he is entitled to see it.
More often, however, a player with a good hand will show first, and the others will just muck, not wanting to give away that information. In that case, if only one hand is shown, that player can claim the pot. If the player with the currently best shown hand specifically asks to see another player's hand, he does so at his own risk--if the hand is shown and it beats his, the new hand wins.
A different case is when all but one player mucks voluntarily. In that case, the player with the last valid hand can claim the pot without showing it. If one of the others asks to see it, though, it can be shown by the dealer.
Also, a losing player who was nonetheless present at showdown can ask to see the hand of a player who mucked if he suspects collusion. This should generally be done as a floorman request, and the floorman may choose to honor it or not, as abusing the privilege slows down the game. In this case, if the hand is shown, the dealer with motion it dead first, and it is not eligible to win even if it turns out to be the best hand.
Finally, if no one wants to show, the general rule is that the last aggressor must show first. If he refuses, the floorman will give him a countdown: "Show the hand or muck it, 3.. 2.. 1.., I declare this hand dead." Then the next player in turn is given the same order, until someone shows and the others muck, or until only one hand remains.