I wouldn't roll a check for something a player has asked to do.
"I try to move silently down the corridor."
"I search the room quickly."
"I hide."
...And so on. I'd let the players make those rolls. If a player rolls badly, prompting another player to attempt the same thing, that's okay. If the rogue rolls a 3 on his search check, I might be tempted to intrepret the roll as, "Boris sifts through the debris half-heartedly and gives up, finding nothing but scraps of parchment." And it's fine if one of the other players isn't happy with the sound of that and attempts a search of his own.
However, as others have said here, there are times when it simply isn't appropriate for a player to make a roll. Take spotting a prepared ambush, for example. If the DM calls for a spot check at some point along the PCs' journey, they know there's something they're looking for, whether they make the spot check or not. Bang goes the element of surprise. If, on the other hand, you have some pre-rolled d20 results on your scratch pad, you can simply apply the next one in the list to the PC with the highest spot modifier, at the moment when the PCs have line of sight to the undergrowth in which the orcs are hiding. If they fail the spot check, they walk into the ambush (or at least move one round closer). If they succeed, you can say, "Boris notices a sudden movement from the bushes ahead and glimpses a bow being drawn. Everyone roll initiative." Incidentally, pre-rolled dice get around the problem of the DM suddenly rolling and then staying quiet (such as when the roll results in a failed check), which also alerts players to something of which their characters would be unaware.
Explain to your players why you would make such rolls on their behalf, that it will improve their game, not detract from their fun or their control over their characters' actions. I did this with my group on day one. Some of the less experienced players were suspicious at first, especially when they found their PCs stumbling into the occasional surprise combat round. However, they've now seen the other side of it, where I point out to them things that their PCs see or hear, because of these secret rolls.
Have fun and good luck.