I generally do not fudge. In my bi-weekly dungeon crawl game, all rolls are open and even the most excruciating run of player bad luck (see: last session) sticks. The stuff they can't see -- hit points and abilities -- I maintain 99% of the time. I must slip up now and again.
In my Jade Regent campaign, which has a totally different feel than the dungeon crawl game, I still try not to fudge, but I let the players have access to Hero Points. Let them fudge. In addition, I am much "nicer" -- i.e. I tend to give them more hints and warnings so they can make informed decisions. Once they decide, though, we play it straight most of the time.
Now a question for the fudgers: say the BBEG fails his save in round 1 and you let it slide. Now the players have burned a major ability (presumably). Do you give it back to them? What about if the BBEG ends up killing a couple PCs -- they wouldn't have died if you didn't save him in round 1, so do you fudge for them in turn (thus creating a self perpetuating fudge cycle)? Do you remain consistent in fudging? if not, how are your players able to make informed decisions about which challenges to tackle versus which ones to avoid? What happens when the PCs make a real choice -- say they want to get 1 more room in, even though they kn ow they are low on resources etc...? Do you fudge for them then, modifying the encounter behind the door to reflect their weakened state?
See, these are all complex questions with cascading consequences depending on the answers. IMO, it is better to stop the problems in the first place by NOT fudging, either on die rolls or encounters. If the PCs press on, and there's a difficult encounter awaiting them, so be it? I might fudge or ignore random encounter rolls as feels appropriate, and I will certainly alter "set" encounters based on the *actions* of the PCs, but "easing up" (or "bearing down"; luck and good play shouldn't be punished) seems less fun than the alternative.