Jonathan Tweet gave some very good advice in a game called Everway. When it came time for a GM to make a ruling on something there were three things to look at: numbers, drama and fortune. He used much more poetic terms than that, but I want to riff off the master, not replicate him, so stay with me here. The idea is that when you are faced with the need to make a ruling, each of these factors may suggest an outcome.
The numbers are the characters stats, descriptors or the like. If the character is a ranger (and this is represented on his sheet) and he wants to track something, then he can probably do it. A strong character can lift things. A smart character can study. Tweet's specific approach was pushed through a lens of dicelessness, but the underlying idea is a solid one, and in many systems it speaks very strongly to when not to roll the dice.
Drama, or more appropriately, dramatic sensibilities are another of the GMs tools. When faced with a question of outcome, which way should things go? Which is more awesome? This is implicitly a judgment call on the GMs part, but the better the GMs judgment, the more likely this would be a good decision.
Fortune, in the case of Everway, was a deck of tarot-like cards which did not reveal a clear success/fail, but rather suggested influences that might be at play, and those influences in turn might suggest an outcome. In other games, this job is handled ably, if a bit more simply, by the dice.
There is no right answer for how these three factors should be prioritized. Every GM strikes her own balance among these, and hopefully does so to great success. Naturally you will have cases where people favor some combination to the point of deriding others, but for the most part that is limited solely to arguments about dice fudging.
Now, I am not here to praise or bury dice fudging. From my perspective, the sanctity of the outcome of the dice is only one of the three pillars, and I will respect or ignore it based on a number of factors, not least of which is what game is being played.
It's a boring argument that goes round and round, so I've decided to strip mine it for something useful. See, the one thing that the die-fudging argument does reveal to me that people have profoundly different relationships with their dice. Naturally, these relationships are intensely idiosyncratic, but I have seen two roles that people assign to their dice: arbiter or oracle.
Arbiter dice are not to be fudged. This is not some simple desire that dice be obeyed, but rather a well thought out approach that combines a respect for the system being used and a desire to introduce the unexpected into play. This is not just about making sure all outcomes are interesting, admirable as that is, but it is also about providing a challenge for the players AND the GM. Because the dice are neutral, absolute, and unpredictable, the GM may find herself having to scramble to keep the game going in the face of a bad (or good) run of dice. A lot of GMs thrive on that sort of challenge.
Arbiter dice work best when the outcomes of die rolls have a concrete mechanical impact which is either binary or directly measurable (such as to hit and damage, respectively). Making alterations to these sorts of die rolls is just a roundabout way of changing outcomes, which invites a certain amount of unintended consequences. More, these systems are usually tuned to handle the full range of outcomes that the dice might provide.
One key point you can look for in these systems is how robustly they can handle a single bad roll. One of the things that classically called for fudging was "Save or Die" situations in the vein of Old School D&D. When a single roll could remove a character from play (especially when that removal was drastically in contrast to the rules of drama) that was sufficiently unfun to demand a little cheating on the GMs part. One of the hallmarks of more modern systems is that things very rarely come down to a single roll - instead they are the aggregate of many rolls over the course of play. The removal of that problem removes the need for fudging, or rather, it does if that was the sole reason to play fast and loose with the dice.
Oracle dice serve a somewhat different purpose. There's an idea in Spirit of the Century called "Testing the Breeze" that reflects on this a bit. When the GM already knows the likely outcome (as determined by numbers or drama) he may still call for a roll of the dice to see how to color the outcome. A GM who buys into this idea may apply it to most of the rolls made in play. These rolls are looked at as ways to color or inform on play, rather than being true decision makers.
Oracle dice work best in games where the outcome of rolls is strongly subjective, as in simple games like Risus. Because there is not much hingeing on precisely what value is rolled, there's not a lot of impact in taking things lightly.
In the strictest sense, oracle dice aren't fudged because the GM has already made all the necessary adjustments before the dice are rolled. This is a subtle enough distinction that I prefer to describe oracle style dice rolling as fudging - the alternative is to open the phrase ot such semantic manipulation as to make it meaningless.
See, the most obvious solution to this divide is to suggest just keeping these two modes clear and distinct and you won't have any problems. Except that's not quite true. If a game is running late and needs to wrap up, an arbiter-oriented game might start bending the rules in favor of pacing. In an oracle oriented game, there might come a tiem when the greatest drama _is_ in pure fortune, an open roll with a lot hanging on it. As much as a given GM and a given game might lean in a certain direction, a specific situation may muddy the waters.
And that leads to what I think is the most important point. Ultimately, what you do with the dice is far less important than understanding why you do it. If you do not have a clear understanding of what you expect from those dice when you pick them up, then you're inviting trouble. The dice will eventually turn in ways you are not ready for, and in your scramble to adjust you are likely to leave things on the floor. When peopel talk about the problems of fudging, this mess is one of the big ones.
But I want to emphasize, that mess comes from a failure of understanding. If I pick up a die and know I'm going to go with what it shows, then all is good. f I pick up a die and know I will be using it purely as a suggestion or as a means to color the outcome that is going to happen, that's fine too. But if I pick up a die and don't know what I'm going to do with it until after it rolls, then the quality of my outcome is probably going to be as random as that die.
1 - For 'more awesome', feel free to substitute in 'a better story', 'more satisfying', 'more appropriate' or whatever floats your boat.
2- "I'm not fudging because I change target numbers, not die outcomes!"