Don't roll unless you mean it

 Another installment in My Old School Manifesto.

There seems to be a lot of disagreement among tabletop gamers about the appropriateness of "fudging" dice rolls. I'm pleased to observe, though, that the practice is much more frowned-upon by folks identifying as OSR or old school, and I agree very much with the principle of NEVER fudging dice rolls. During actual play*, don't roll -- don't even TOUCH the dice -- unless you mean to abide by the result.

*It is absolutely acceptable to roll dice during game prep activities, such as creating a dungeon, for the purpose of inspiration or a sort of writing prompt, and then to disregard or modify the results. We're talking actual play here.

By not rolling the dice unless you mean it, you preserve their objectivity. Players know you're not going to bail them out or screw them over because of any biases or preconceptions about what "should" happen.

If you believe strongly that a particular outcome should occur, just announce what happens and move on. Don't roll and then say, "No, that wasn't what should have happened," and overrule the dice. That just signals to players that dice rolls are essentially meaningless. If you're going to engage in DM fiat (and there are times when that is appropriate,) OWN IT. Transparent fence-sitting is for cowards.

And for the love of monkeys, don't engage in ex post facto modifier nudging to get the result you were secretly hoping for. ("Oh, you needed a 13 to hit and you rolled an 11 - missed by 2! But wait! The monster was standing in slippery mud, so it couldn't dodge very well; +2 bonus! You just made it!") Be up front about the conditions of the roll, and then stick to them. (It's a bit different in the case of clearly codified by-the-book modifiers, e.g. the player points out that his character's bow attack was at short range and should have received the +1 modifier specified in the rules. It's NOT OK for the DM to make rulings on non-standard situational modifiers after the fact, though, or for players to lobby for them to bolster an already-made roll.)

Apply the principle of Don't Roll Unless You Mean It to every roll you make during a game session: attack rolls, damage rolls, saving throws, thief skills, wandering monster/encounter rolls, reaction rolls, even rolls for treasure if you do those in-game instead of during prep time. 

When can or should you leave the dice alone? 

• Any time an outcome is not seriously in doubt, but usually only when it favors the players. When a 5th-level party encounters a single goblin, there's no harm in simply declaring the party handily defeats him, either killing or capturing as they prefer. It's OK to tell the thief, "It's a very shoddy lock, and you easily pick it; no roll needed." (In contrast, it would go over very poorly to say to the 1st-level party encountering a frost giant that it pounds them all to pulp without ever rolling an attack, even if that's almost certainly what would happen. It's likewise poor form to tell the thief, "You fail to open the lock" without rolling, even if the odds are low.)
• Any time you're sure of what an NPC or monster will do in a given situation. Reaction rolls and morale checks are handy tools for when the DM has no strong opinion on what creatures will do in a given situation, and they're great for subverting expectations and making you think outside the box, but as DM, you do control every non-player entity in the game. It's your prerogative, so when you choose to exercise it, don't muck about with dice first. Own it 100%.
• When a dice roll has no meaningful or interesting consequences. The first roll to open a stuck door determines whether the party has a chance to surprise anything on the other side of it. Subsequent rolls are pointless and anticlimactic: the players can try again and again until the dice indicate success, but you may as well just say they succeed after banging on it a bit more, because the monsters know they're there either way. It would also be largely pointless, for instance, to roll reactions for every merchant from whom the PCs want to buy something, or to make a PC roll a Dexterity check to cross a rubble-strewn dungeon room when the only result of failure is that the PC stumbles. 
• Events or content that are normally procedurally generated, e.g. wandering monsters, treasure, or weather. It's perfectly OK to pick a monster from the list without rolling, to say it's carrying 15 electrum pieces and a silver-bound drinking horn, and to declare it's raining in the campaign world today.

There are probably other situations I haven't thought of, but hopefully you get the gist. In all cases, though: no backsies. Once you decide to roll, or call for a roll from the players, the result of that roll is law. The die is cast, as the saying goes, both figuratively and quite literally.