Usually, no. I don't tell the players what AC they need to hit on a monster either. I'm of the DM school of "fudging when necessary" (already discussed to death in other threads). If I tell them the DC, I can't fudge. However, there are times where I do tell them the DC because I feel it engenders a certain amount of drama about the roll. I won't do it when life or death is in the balance (that's when I usually fudge).
This is my exact style, except for the last part. When the chips are REALLY down is when the players need to know we play for keeps. (I fudge like hell, for drama, up to that point.) Then, when we all know it is life or death, I call out the DC, have everyone (including myself) roll out in the open, in the center of the table.
Basically I'm praying to the dice gods to carry the PCs through at that point. The last con I was at, we did exactly this, and the PC (out of healing surges and down to single digits HP) defeated the unholy snake god with a natural 20.
Perfect D&D moment made possible by a lot of cheating.