I feel like I most often fudge in my storytelling... if a player offhandedly mentions a cool idea like "I bet this BBEG was this other BBEG's apprentice" ... even if no prior relationship between the two existed in my head canon, BOOM! there is now a mentor-apprentice relationship. Basically, if my players speculate about something and I think it is logical and/or cool, I'm likely to steal and incorporate it, even if it wasn't in my head canon when I wrote the scenario originally. Players sometimes shape the world more than their characters... just by opening their mouths.
Or if, for example, one of the players suggests "man, that king was a jerk... wouldn't it be funny if the princess we're trying to save doesn't WANT to go back to her kingdom" even if the final outcome in my head was, "princess returns to kingdom, PCs get rewarded with a land grant and become minor nobles" I'm definitely going to be scrambling to change the ending to "princess convinces PCs to let her join the party and now they are outlaws that can never go back to that kingdom" and maybe reward one of the PCs with, say, a unique magic item the princess gives them... or have the princess become a magical mentor or a love interest or whatever ... or maybe be revealed as a Shapechanged Dragon that joined the royal family out of boredom but now wants out of the ratrace instead.
And generally, I'm of the opinion that story-based fudging, especially when the PCs encounter some sort of resolution they had speculated about for weeks but I had originally thought would be something different (or perhaps I based it on their speculation but with a twist) tends to be very satisfying for the players, who feel like the world meets their expectations and so it makes sense. So generally, I consider this to be a good form of "fudging."