Normally when I am called to a table and players ask me "who has to show first?" my answer is "whoever wants to win the pot" and I walk away.
That being said, let me present a few scenarios and I would like to know how your house handles the issue when players are not opening their hands voluntarily and an order of show is enforced. The first couple will be the basics, while the second two will change it up slightly. In all cases Player A is the under the gun player on that street, clockwise of the button and B and/or C are clockwise of him.
A) On the river, Player A checks, Player B bets, Player A calls. Who must show first?
B) On the river Player A checks, Player B checks. Who must show first?
C) On the turn, Player A checks, Player B goes all-in, Player A calls. The river is dealt. Who must show first?
D) On the turn, Player A checks, Player B checks, Player C goes all-in. Players A and B call. The river is dealt. Players A and B both check. Who must show first?