I roll some of my die rolls in the open. Some of them behind the screen. Which ones do I roll where nowadays?
Generally, I'm pro-"fog of war."
What I roll in the open are generally rolls where the range is obvious, or at least easy to discern, and the results are concretely obviously to the players.
Damage Rolls - Mostly for the excitement and terror factor. I toss the dice over the screen, sometimes without even bothering to look. "Take that much, +4, cutting."
I think it's much easier to gauge how hard you got hit. "Man, that guy's got a lot of mustard on that punch, (but I got grazed/it didn't land square/I took all of that.)" Plus, it's not a terribly revealing number. Knowing your opponent does 1d+1 or 3d+4 or whatever doesn't really change too much - you have a rough idea already from how much gets past your DR. It's not often people will take a hit instead of trying to defend, so it doesn't change the behavior of the PCs.
It also helps keep me honest. I don't fudge die rolls often, if at all*, but I do get lazy about calculating damage. If I tell them the base roll and let them figure injury, that laziness is sidestepped. I don't need to ask their DR, do the math, etc.
Hit Location Rolls - Not always (because it's slower than if I dump the dice in front of the hit location chart) but sometimes I'll roll a random location in front of the PCs. It's not like you don't know the results when they happen.
Consequence Rolls - If reinforcements show up because of PC noise, say, I'll roll right in front of them. Same with most other "you caused this" kinds of rolls - traps they set off with a random number of strikes, falls into a pit with a random number of spikes, etc. - I roll in the open.
Unconsciousness checks by NPC allies get rolled here, too, because it adds to tension in a way that "He made it" or "he missed!" doesn't. They usually know the stats for their allies, anyway, since letting them know speeds the game.
What I roll in secret are things where the numbers aren't really obvious, and which easily can change behavior. Here are some examples.
Skill Rolls for enemies.
Knowing the skill of an NPC in GURPS tells you most of the things you need to know in combat. Knowing an opponent has Skill 15 tells you a remarkable amount about his possible defense rolls, what targets he can attack at what odds, the utility of your feint, how much Deceptive Attack is worthwhile, and more.
What I will announce is margin of victory or failure in a contest, if that matters (say, a PC Feints and makes his roll by 10. I roll for the NPC and make it by 4, I'll say "You win by 6.") That's laziness more than anything else, because now I no longer need to track the number, my players will do it. ("Don't forget, he's at -6!")
I'll also colorfully let you know how relatively good the guy is. "He's clearly very good." You'll pick up some numbers just based on what someone does. "He cchops at your neck and hits, Deceptive Attack -4." You already know he's got a 19+ skill, or 17+ and some variation of Targeted Attack, so use that knowledge wisely.
Some of this can be poo-pooed with "my players don't meta-game." But if they don't, they don't need the numbers. So it's better to keep them away from everyone - the ones who'll use them and the ones who won't. In my opinion, anyway.
Defense Rolls for enemies, for the same reason - you don't need to know what it is. If he barely succeeds, I might say so, but you're not getting numbers. They affect what you know you should or should not do - and I prefer to leave that up to player strategizing and cunning, not number-crunching based on raw data I feed you.
Resistance Rolls for enemies, for the same reason. Succeeded, failed, that's all you get to know.
Everything is done descriptively. You might know the guy is staggered by your hit, or that he's barely standing (or seems to be), or that he's really, really good at hitting your eyes while standing on bad footing. But I'm not rolling in front of you because it's too easy to reverse engineer the numbers. I give out lots of description but not a lot of crunchy hard numbers.
And those numbers are the GM's world, in my game. Your world is your PC, those damage dice tumbling over the screen, and what you see in your head based on the maps on the table, the minis on the map, and the descriptions I give out.
For me, that's where the fun is, not in knowing the stats of the bad guys. So I conceal all the rolls that might make them transparent to you, and, in my opinion, less interesting in the long run.
How about you guys? Are there rolls I make behind the screen you'd prefer to do in front of everyone, or vice-versa?
* Although I sometimes roll dice and ignore them entirely, to maintain the illusion that there is a chance even when there is a certainty. Hey, you don't always know there is a certainty.