I like the check on the river because usually you aren't going to get called unless you are beaten anyways. Against average to good players that is. (Although I'm amazed at some players that I've played against who call all the way to the river only to fold to one bet on the river when they have pot odds to call. Makes me smile
If you bet and the other guy folds what do you gain? You risked a bet to win a pot you probably would've won by showing down anyways. Check calling is more of a read on the player you are up against I think. Is he loose or tight? Bluff much? etc....
my humble two cents
ChiefBigtoke