The concept of "fudging" die rolls as a dungeon master is a difficult thing to discuss without misrepresenting my position. The dice absolutely have to be sacrosanct. The random number generation aspect of the hobby, in conjunction with a robust set of rules, provides verisimilitude, and verisimilitude is what makes a roleplaying game a roleplaying game, and not a collaborative improvisational storytelling coffee klatch. I hate the term "fudging;" in an attempt to make the act sound like it is not as serious as cheating, I think it trivializes a devastating responsibility.
The dungeon master cannot cheat. I do not mean they should not cheat; I mean that for a dungeon master to cheat is an impossibility. You might just as easily say that the Chance deck in Monopoly cheats, or the board text in the Game of Life. The dungeon master is not a game player, they are the living execution of the rules. To suggest otherwise calls into question the very core of the hobby: what makes it fundamentally superior to video gaming.
A dungeon master can make mistakes. A dungeon master can be terrible. In more contemporary parlance, the dungeon master is the CPU that runs the game's code, and they can be susceptible to glitches and overheating like any other processor. But they have a substantial advantage over a computer -- they can think.
Ignoring the results of a die roll is not something that should ever be taken lightly. It is not a betrayal of trust, it is the essence of trust. It should only be invoked when the alternative is miserable, and a good dungeon master is trusted by their players to make that judgment, not to always be honest. Honesty is a terrible trait for a storyteller to have. No one wants honest stories.
In an honest story, the hero dies when he rolls a natural 1 on his Perception check and has his throat slit in the night by a kobold. In an honest story, the climactic encounter against the villain is over in a round when he fails his Intelligence save and the Mystic mind-controls him off the balcony and onto the rocks ten stories below.
If you'll excuse the rhetoric, it blows my everloving mind that anyone could ever trust their dice, or authors whom they've never even met, to run their games for their players better than they could. The system is not worthy of trust. It is not sapient; it is not conscious of the events at the table; it is a poorly playtested and edited set of rules in a book written long before the campaign even began, which relies on shoddily manufactured plastic polygons to generate simple numbers for the abstraction of the incredibly complex interface of aptitude, skill, and chance.
You need a system to adjudicate all the crap that doesn't matter, for a sense of realism, and that realism is important. But if you let realism decide even the most critical elements of your story, everyone is in for a dull ride. If you're a good dungeon master, when the chips are down the system doesn't matter. If you're a bad dungeon master, no system will save you.
For the love of Gygax, if it was as simple as books and dice, players wouldn't need dungeon masters. I'm not saying 'don't roll' -- I am definitely not saying 'don't roll' -- but if you roll and the result doesn't make good sense, don't 'domo arigato Mr. Roboto' it, step up and KICK ASS.