I'm much more likely to fudge hit points than die rolls. Many of my monsters are invented and unique and on a couple of occasions I've left off decisions about hit points until combat started because I was wavering regarding how touch the fight would be. I can remember dropping a 7 HD monster to 5HD on the fly once, and I've also arbitrarily gave a monster 20 additional hit points.
I fudged die rolls a couple of times thinking it would make the game better, and regretted it each time, so now I just don't do it any more. I usually roll in secret, but sometimes roll in the open for dramatic effect.
In the beginning of my DM career I fudged the hell out of the dice. It ended up that I rolled the dice just so my players heard the sound of dice rolling (hyperbole). I started to hate it with a passion. But my players preferred it that way.
Nowadays I play online and just roll in the open. Let the dice "roll" where they roll. It's much more exciting for me (and maybe my players).
I'm rolling in the open. I voted 'once or twice', since I remember one encounter in our group's D&D 4e 'role-playing camp' vacation in which I ignored an elite brute monster's rechargeable skill because they party had such an abysmally bad start that anything else would have resulted in a TPK, ending our week of roleplaying early:
They had decided to squeeze through a crawlspace into a room guarded by several crossbowmen and their berserker leader and failed their stealth checks, so one after another they were first pelted by several bolts before being taken down by the berserker. When they realized their mistake it was already too late to withdraw...
Apart from that I'm a firm believer in 'self-correcting party composition', i.e. my adventures tend to use a range of different 'standard' encounters types that each require a different approach and/or skill set to be successful without expending excessive resources. Parties (or more often individual characters) tend to fail (i.e. usually die) until they represent a viable mix of classes and roles that can deal with them.
I used to fudge quite often - I spent my early years of roleplaying running various oWoD games that explicitly encouraged fudging and other illusionist techniques.
Later I realized that there are much more fun ways of playing and running RPGs and I started using games with rules that worked instead of rules that required me to work around them. I switched to rolling everything in the open and stopped fudging.
I usually roll behind the screen. It keeps some of the mystery alive. Players are pretty quick at determining monster AC's and saves viewing rolls in the open. In addition, every once in a while I'll find that an encounter was designed a bit too tough so I might fudge the bad guys' rolls down a bit.
In my early days of GMing, quite a lot. Now, I prefer to roll in the open so players are less likely to complain about bad luck if they can see the roll themselves. In so doing, I'd get caught fudging. As far as I remember, recently, it was only once, in the PBMB game.