I was wondering what is the point of rolling behind a screen as a GM?
If nobody can see the roll then I could claim that I rolled any number I require, right?
If I would have to show the roll, then why would I roll behind the screen in the first place?
I do like the idea that nobody hides the rolls, but there might be scenarios where it makes sense to roll behind a screen, not sure yet when this is necessary.
In what situations would it be an advantage to roll dice behind a screen?
Sure, you could cheat as a DM. However, in an ideal case,
You need to understand and practice that to gain their trust. And to gain trust (and lots of practice) in your own story-spinning abilities. You're playing a game together, a game that has rules than bind you as well... unless the story calls for you to cheat. For sometimes you need to cheat.
You roll in secret to keep certain things secret, and to achieve suspense. But you roll, and you obey the roll.
You cheat (sorry: you may want to cheat) to prevent accidental deaths of PCs, and to avoid the utter derailing of the story (not when the PCs come up with a clever solution that cuts through the Gordian knot of your story, mind you), and... and that's about it, mostly. Otherwise, if you cheat, you're spoiling the game. Your own game. It's just as much fun as going berserk in an FPS (Quake for example) using God Mode. Not much.
So, this is it, in my opinion. You'll find finer details, other points of view, etc. in the other answers, of course.
You're not playing against your players. If you are, do it with their consent... but I think in that case you're not really playing a role playing game. You're playing a boardgame, of sorts. Which can also be fun, as long as everyone is having fun. And don't cheat. Unless you must. :)
One more thing: sometimes you just roll behind a screen for the fun of it. That's the suspense part. You roll so that they think something is happening. But the score you roll doesn't matter in these cases. It's just the act that they... need to see.
One of my favorite things about the 7th Sea GM book is...
Rule 1: There are no rules
Rule 2: Cheat anyway
As the DM/GM/ST nothing you do truly constitutes cheating but it takes away fairness in games where the outcomes are determined by dice or entropic factors. Ultimately, I find that regardless of the system, DM transparency is truly up to the DM in question. Yes, D&D might encourage a DM screen but ultimately screens are cheatsheets for me and I don't use them as dioramas so much as a loose packet laying flat in front of me. I tend to roll in secret though because I know my players get a certain sense of suspense (dread) whenever the dice drop.
For me, the most important veiled rolls are for the players themselves as an anti-metagaming tool. Did they roll a search check? Act like you're rolling a stealth check and smile "harmlessly" when you tell them they find nothing. Players ask/do something you didn't plan for? A good decoy roll stalls a few seconds to make up your mind but blame the NPC if you feel guilty. When they don't even see you pick up the dice they know they've won and whether they realize it or not they will meta their way through thanks to de facto numbers.
Are these things deceitful? Yes. Are they cheating even by mechanical standards? No.
Also, I don't know what your table is like but some players are smart and once again, unintentionally meta their way through problems. "He rolled a 15 and scored 17, so the monster has a +2 at this" can get frustrating when they're watching the dice. Knowing the full abilities of something numerically can be a hindrance, especially if you want to use special abilities and not seem a cheater by that rote either.
In summary, hiding your rolls does not necessarily mean clandestine things and it's up to you if/how you use them.
Sometimes Rolls Should Be Secret
The point of rolling behind the screen is that you don't want the players to know what you rolled. This is most used in opposed checks and skill checks. Do they really need to know how well the NPC is rolling Bluff, or if they were seen while hiding by an enemy Spot?
No. It's more fun if the players don't have perfect knowledge of things they shouldn't know.
This can also be used to keep people honest, by rolling for no apparent reason. It makes them think there's traps, or spies, or something in the area they should be worried about.
Not every roll has to be a secret, but you want to provide at least some mystery about what's going on and how well the players are doing in trying to pass off their forged documents.
Fudging Rolls - Best done Rarely
While it's true that you can claim you rolled any number you want, it's best not to do that except in exceptional circumstances. I've done that once, in a case where a player was having truly awful luck one night (failing everything they tried) and I rolled four criticals on them in a row. I fudged a couple of those down to normal damage because simply wiping them off the map like that wasn't fun for anybody.
It's an ability that you should use very sparingly. If the players start to think you're just making up rolls to do what you want, they may consider that cheating and get angry.
Opposed skill checks
When players are rolling diplomacy against an NPC, they are trying to bluff/deceive an NPC, or are trying to use insight to not be bluffed or deceived themselves and you choose to handle it through dice (vs. roleplay) you should roll for the NPC in secret.
NPC actions occurring off-screen
NPC actions may occur outside the current view/hearing of the PC party such as setting up traps, NPCs hiding for an ambush, NPCs trying to influence city councilmen against the PCs etc. Whenever such a thing would occur roll in secret.
In D&D 4E: Monster Power Recharge rolls
Some monster power stats will have dice side icons next to a power. These powers have the chance of recharging after they have been used. You roll to see if the power recharged at the start of the monster's term, there's really no reason for your players to see this roll.
Rolling to monster locations & treasure distribution in a dungeon
Sometimes when you run modules and other adventure content the actual locations of monsters and treasure in the dungeons will be randomized (4e's Lair Assaults is a prime example of this). When the PCs enter the dungeon area you'll roll to see where everything goes.
Rolling dice to scare your players to think any of the above are occurring
Hidden rolls are a great way to intimidate players and spice up an otherwise slow or boring moment because the simple sound of you rolling dice and making notes of the results will cause expectation in your players creating tension.
There are already good answers that covers most of the cases when rolling can be useful. I will address it from a slightly different angle, that is, this specific question:
If nobody can see the roll then I could claim that i rolled any number I require, right?
You roll behind the screen because you don't want players to see too soon the outcome of the roll, for many reasons (see Joshua's answer). That's the simple ideal case. You could fudge the result, yes, but you don't do it because your players trust you. And because your players trust you, you can roll behind the screen without them getting suspicious.
Sadly, many GMs roll behind the screen just because they want to cheat the outcome, because they want to railroad the PCs in some way. There are even many RPG books that encourage you to do that. In my opinion, that's poorly GMing. If you cheat with the rolls, and most of the times it's evident even if you think that it isn't, your players will start to distrust you, and the dynamic with your players will be less satisfying.
So, returning to the question. A GM should roll behind the screen when he wants to keep the roll secret for some time. A GM shouldn't roll behind the screen to fudge the result.
A pair of answers mention some cases where cheating is legit, mostly when you try to prevent a PC's death. I disagree. Be always honest to your players. If you want to avoid the death, don't make a fake roll. Just don't roll. Tell your group the PC has fallen unconscious, or any excuse. If needed, explain your group you didn't want a character to die only because of bad luck. They are supposed to be your friends, don't lie to them.
In general, there is almost nothing to be gained by rolling behind the shield unless you're not using the rules mechanics.
There are a few cases, especially in old-school play, where the keeping of certain information hidden is worth the inherent distrust triggered by rolling behind the screen.
If players should not know a specific duration, it's fine to roll it behind the screen. The truly scrupulous GM will roll it, and then cover it until relevant, and then reveal it (but that requires extra dice).
Are suspense and lack of player knowledge.
The temptations to not use the rules, to not actually read the dice, and to announce results based upon personal biases. All of which can, if noticed, destroy trust in the GM's fairness.
The idea of rolling behind the screen is to prevent the players from knowing whether or not they've succeeded - when the result isn't immediately obvious to the character. Examples include:
Basically, it's a tool for when a player shouldn't know how well the other side (whether it be an enemy or a natural obstacle) is doing against them.
This isn't always necessary. In fact, you can forgo behind-the-screen rolling altogether if you wish, and make all results public knowledge. The duty to resist metagaming then lies in your player not abusing the knowledge that you've rolled a die.
Or, in the opposite direction, there are ways to conceal that you've rolled at all. One popular way is to simply write down a list of results ahead of time and use them as the need arises (while still rolling for those things that don't need to be secret).
Whether you roll behind the screen or not really depends upon your own personal DM style, and the play style of the players you have at the table (and whether or not you trust them not to metagame)
To add to some already great answers, I wanted to add my thoughts on the subject. In short, the main line of logic that will run through all of my answer is that you should decide for yourself according to the things you are trying to get out of the game.
We participate in roleplaying games due to many different reasons. Some of us are there for the story, some of us are there for the fights and the killings, while others are there in order to simulate some kind of experience that they may have encountered or that they wanna see how it will roll. There are of course many other reasons to participate in those games. With that being said, cleared and acknowledged, let's go to answer your question, which is "When should a GM roll behind a GM screen. The answer is quite simple: you should or shouldn't roll in secret according to the things that drive you ("you" the GM and "you" the entire group) to play.
If for example, you're playing for the sake of the story and the drama, some of the rolls should be kept in secret so you'll be able to "adjust" them a "little" bit in order to create a greater sense of drama. Sometimes, that one just doesn't fit for the things that you've created together and they should destroy the story. Those you should avoid, and by not showing the players the number you can do it without them knowing. Those cases should be kept to the minimum, of course, as many a time the dice have a part in creating the story and the drama too. I f the bard at the tavern, who should be one of the better lute players in the realm, has a really bad day (rolled a 1) it can be the spark of a new story, an opportunity for the PCs to shine (their bard can surpass him and be called to the king and/or queen, for example). In short, it gives you the possibility to "adjust" the dice in order to serve a greater drama. This option should be carried carefully and with a great understanding of the price of such a way.
Sometimes you should roll in the open, too. If (to continue the example from above) the PCs are in a fight that carries no important role in carrying the sense of drama, rolling in the open will help you to create the sense of fairness. It can also, again, be the spark of a new story. Sometimes, it can serve as an excuse for a great defeat, as they saw what just happened, what just did that.
In games where you play for the sake of the** game**, for example, there is really no need to role behind the screen. After all, no one is playing for the story, and in games there might be some surprises. The great swordsman might miss the easiest opportunity to hit ever seen and even the lousiest commoner can sometimes hit (or even kill) the great hero.
So, to conclude all of that, think about what drives you and your group to play and based on that decide whether a roll should be made hidden or out in the cold.
Whatever benefits or drawbacks there are to rolling behind a screen, they are a moot point if you only selectively roll behind a screen. Rolling behind the screen for an occasional roll does not build suspense, it builds suspicion that you are cheating.
If you always roll behind the screen, there is much less of an assumption of cheating - it's just how you roll. If you never roll behind a screen, then this is an entirely moot point.
