In other cases, if I "fudge" mechanics or the like, I always make it clear to the party that something weird is happening, and provide them with the opportunity to learn what it is, and how they can respond to it (whether learning to prevent it in the future, making use of it themselves, weaknesses induced by it, etc.) So, to use the classic "the party got a lucky string of crits and blew away the cool boss fight I made," if I felt it was that important to keep the fight around long enough for something to happen, I would make up something and the party would be able to observe it. E.g. if it's an evil wizard, "You land crushing, telling blows--the wizard is caught completely off-guard by your attacks. His face contorts into an ugly expression as you land what should have been a lethal wound, yet somehow, he still stands. He draws from his robe a golf ball-sized globe, which seems to be filled with fire and...possibly blood? He crushes it in his hand and you smell burning blood and the faint trace of brimstone. His wounds are knit shut by sutures of fire and his eyes glow with a baleful light. He's clearly determined to defeat you...no matter what it might cost him." That makes it so the players know their actions SHOULD have worked, but something got in the way (in this case, the powers of hell). It gives them the opportunity to learn, and later on, prepare.
Note that I used quotes above on "fudging." I do not consider this an example of fudging proper, because (a) it isn't secret, I'm telling the players something is happening, and (b) the players have the opportunity to learn from it. They might bungle that opportunity. Such is the nature of any dice-based game. But they have something to work with. It's very, very important to me as both a player and a DM that that opportunity exists.