This is something I've noticed in some live plays I've watched... some DMs tell their players the DC of challenges before they attempt them, which can create some interesting tension with the roll as the character has a concrete goal they're reaching for. However, I've always hid the DC, since in-character there's not like... a number that the character has to reach so I try to just narrate how well they did on a challenge... liek if they failed horrendously I narrate that, but if they get extremely close but just barely miss the DC I narrate how it's only the slightest issue that prevents them from succeeding, and they can plan from there. On the other hand stating the DC out loud sets it hard in stone... everyone at the table knows everyone else is being honest in those situations... I have to admit I've fudged the DC a few times in the past during important story stuff.

Generally no - but I don't particularly hide it, either.

I might muse aloud a bit as to how difficult what they're trying to do is, as I'm figuring it out - but I don't usually give the final number.

Yeah I do occasionally give the players a warning, especially if it's an obviously bad idea they're mostly doing as a gag. Something along the lines of, "Okay, but just so you know, the DC of that is going to be really high"

It depends on the kind of challenge. If they attempt something that they could probably guesstimate the difficulty of, then yes. Picking a lock, especially after an successful checking for traps, yes. The checking for traps, no.

I never tell them. I’ll give a hint like, it looks like it should be very easy, but never the exact number. 
The closest I can think is in the case of a saving throw against an area effect where its something like “if you beat a DC 14, you take half damage.”

I may, however, tell them the DC after in some cases.

E.g. - the Rogue is going to pick a lock, but there's no time pressure, and no penalty for failure. A lot of DMs would say not to even call for a roll at that point. I still do ask for a roll, because - even though they are going to get through the lock as they just keep trying - the gap between the roll and the DC has other secondary effects, in my mind. If the Rogue missed by a lot ( 5 or more ), it might take 10-15 minutes, and the lock is scratched up pretty badly ( meaning that when the Patrol comes by later, they have a lower DC to noticing that the lock has been tampered with ). If they succeeded by a wide margin, then they did it quickly, cleanly, and left nary a trace. 

If it’s something they (as players) would know, like the DC for reading a Spell Scroll above their level then I tell them. For DCs I set, no, I almost never tell them.

If the character would know approximate difficulty (easy, hard, etc.) I’ll tell the players that much. If it’s a more abstract roll with very specific results (how much money they make from a business, etc.) I’ll give specific numbers and results because it’s useful for them to understand the various potential outcomes. But for the most part, I see no reason to provide this information.

I actually don’t usually even outright say whether something was a success or a failure; I just narrate results and let the players interpret it as they will. Part of the reason for this is that I very often don’t actually set specific DCs and instead wait for the roll and decide after the fact how much I think that roll is worth. Contested checks are different and much more specific of course, but the very fact that it’s a contested check is a great reason not to reveal target numbers.

I mostly don't tell people DCs for ability checks, but I rarely keep save DCs secret, and I'll tell people ability check DCs if it's something they would reasonably know (for example, a athletics check to climb a wall isn't a secret, unless the wall has some secrets).

Quote from Vedexent >>

Generally no - but I don't particularly hide it, either.

I might muse aloud a bit as to how difficult what they're trying to do is, as I'm figuring it out - but I don't usually give the final number.

 This is what I do.

I'll say something seems pretty easy or very hard, or I might ask, "Are you SURE???" if it's something highly inadvisable but I don't give DCs in general.

Sometimes it is obvious. The rock face is a hard climb. The grumpy bear is a moderate challenge. The lock on the Sultan's treasure room is very difficult.

Sometimes it is not. The characters have never met the SUltan, so they don't know how hard it will be to persuade them to finance the expidition.

If it's something where they can assess the difficulty before attempting it, such as climbing a wall, then yes.  If it's something where they cannot, such as searching for traps, no.

I don’t reveal the DC, although the way I narrate may hint at how close they came to achieving it. Or how horribly short they fell.

I don't tell my players the DC's needed but give a hint of how well or how poorly the outcome of their roll is in regard to their saving throw.  I use this same methodology for creatures AC by never outright telling them what they need to hit.   Usually, the players will figure what that base number is on their own if the DC is called for on a frequent basis (ie Gazer who's attack are primarily all DC-based attacks.)  

Quote from BigLizard >>

If I did it right, the players aren't even aware they just made a skill check.

 Do you make the roll for the players in those situations?  

When I play, I love rolling dice. And I like knowing what I need to beat. If it's a number I can easily beat, I feel competent on my character's behalf. If it's a reach, it adds tension and I try to pull resources from my party: bardic inspiration, guidance, bless, maybe a help action...

So when I DM, I generally give out the DC for rolls, unless I think it adds mystery. As I said above, looking for traps is one of those times when I don't want my players to know if there are any. They don't find a trap, is there none there, or was the roll not high enough? Disarming the trap, however, is something they should have the DC for, as they have found the mechanism, and they should be able to judge how difficult that would be.

There are also many mechanics in the game where you can use a resource 'after you roll the die, but before the outcome is determined'. This means they player would need to know as soon as the dice stop rolling, if they need to spend that resource.

On a side note, I discovered that Beholders and their kin make for excellent opponents as they allow players to roll more dice. It is much more exciting to roll a saving throw than 'merely' subtract hit points from your character sheet.

Lunali's got the right of it.  Certain numbers should be easily accessible to the player, as those numbers are abstractions of things the character could easily recognize.  A well-trained, highly experienced fighter should be able to estimate an opponent's armor class within a point or two just by watching them for a moment, and certainly after taking a swing at them.  Similarly, someone trained in Athletics should be able to judge the relative difficulty of a climb or a jump within a point or two.  Similarly, I find little point in concealing the DC of a saving throw - the character can feel whether or not they succeeded and how hard they had to work to do it, and giving the players the specific number can help them make interesting tactical decisions.

In cases where the player has no idea what the difficulty of a thing should be, then obviously don't give them the number.  A lot of the time though, if you're not willing to give the player the number, you shouldn't be letting them roll the d20.  Any check like that is best handled by the DM asking for the player's modifier and rolling the check behind the screen, but a strong majority of tables object to that.  Finding the right balance for your specific game is part of learning to DM.

If they ask, then no.  I might say something like, “from your knowledge and general experience, you’ve never see. Something like this before” or change the word a little if it’s a low DC.

im just conscious of not wanting to sway them or railroad them into something or not. 

I figure that if the character would logically be able to guess their chances of success, the player should be able to do so as well; thus, I'm perfectly willing to reveal DCs for most routine tasks, but if there are significant unknowns I'd give them a range of difficulties.