It depends. In some cases, like jumping, the DC is typically based on obvious factors. If the PC needs to jump over 2 squares, then he should know the DC. Knowing how the rule works equals knowing the DC. If there are noticeable factors like say wind that might impact his jump, he should probably know about those too.
On the other hand, something like Insight or Bluff is typically going against an unknown circumstance, so the players don't know the DC.
Of course, I might be tempted to tell people the DCs - or at least relative difficulty - in a full blown skill challenge.