Noisms over at Monsters & Manuals has a very sensible post about attitudes towards the use of dice in RPGs. I'm not entirely clear why anyone would find it controversial, especially when he explicitly does not pass judgment on either diceless gaming or games where "story" has primacy. My own advice is this: never roll dice (or make the players roll them) if you're not prepared to accept a negative outcome. That's why I don't include monsters, traps, or magic items that require saving throws unless I am willing to allow them to harm, injure, or kill the player characters and/or their henchmen/hirelings should things go awry. Conversely, I roll all my dice out in the open, lest I fall into the temptation to ignore the results.
I recognize that I have a higher than normal tolerance for letting the dice fall where they may, but I share Noisms's bafflement at fudging the dice. I think there are many perfectly valid reasons for not rolling dice to determine the outcome of an action in a RPG, but, if one is going to roll dice, why not accept their results?