I'm a big proponent of making things dramatic where appropriate. I've also been DMing long enough that I have a pretty good sense (though I'd never claim it was perfect) of what my players find fun and exciting.
I've fudged rolls in the party's favor, but I've also fudged rolls against them. In both cases, it was to prevent something from proving woefully boring or anticlimactic. I try to make sure it evens out over the long run, however, and I never fudge to stupid degrees. (I won't cheat the players of a hard-earned victory, for instance--but then, I wouldn't anyway, since that doesn't fall into the non-dramatic category.)
In either case, I fudge only rarely. 95+% of the time, I prefer to let the dice fall where they may.
I use a screen if we're sitting at a table. Usually, we're just spread out on chairs and sofas, in which case I just roll in the plastic case I keep my papers and dice in. In either case, the players cannot see the dice. Sometimes--such as on particularly important rolls, such as a life-or-death save--I'll roll in the open to heighten the tension.