(this was originally - in part - responses of mine to a thread on G+)
I run my games via G+ Hangouts / TableTop Forge - my rolls are in the open, except for secret door checks / wandering monsters and the like.
The world is not always a fair place, and without risk the game (it is primarily a game, not a storytelling experience, although the story should evolve naturally through play) is bland.
How can there be excitement for overcoming great odds when fate and chance has no place in the equation?
I'm willing to improvise and let my players think up solutions / actions / flaming mine carts into orcs and the like that are not strictly covered by the rules - heck, I encourage it. That's the extent of my DM Fiat - letting the players find methods to increase their chances of success.
If the game uses dice, the dice are there for a reason. Denying them the ability to impact the course of the game removes much of "the game" from the experience.
I trust my players to play through the dice rolls, good or bad.
I am expected to do the same.
My players don't want fudged dice rolls, in their favor or against them. Sometimes they fail when the odds are heavily in their favor. Sometimes they unexpectedly succeed. Same with their adversaries.
For my group, that is part of the fun. Well, that and beer and derailing the game with outside the game talk. But that's how we roll - with honest rolls.
By fudging the rolls, you are moving from RPG to Storytelling. There is a huge gray area where they overlap, and fudging of dice is a part of that IMO.
That to me is the issue - are you playing a game or a looking for a storytelling experience?
My fear is that fudging dice rolls for "the story" takes importance away from "the characters". My feeling has always been that "the characters" should always come before whatever story I may have in mind, and that won't be the case if I fudge dice rolls.
Besides, I expect my players to be honest with their rolls. The least I can do is the same ;)