Very seldom do I show my cards other than during a showdown. I'm pretty much a "You've got to pay to see 'em." type of gal.
Though at a showdown, I always turn my cards over and show them because that person has paid.
Sometimes, and not I will show them if it is something impressive like four of a kind, straight flush, full house, etc... when the other player folds. I think that they like to see that because they know that they did the right thing, and other players just like seeing a big hand. One time up at the Filotimo another player leaned over to me on either the turn or the river and said, "If I fold will you show me your cards?" He folded, and I showed 'em.