Do you like rolling?

[Herobizkit]

So I've found myself more and more often in the following scenario. The DM presents the group with a situation outside of combat and gleefully calls for a die roll, perhaps for a skill check. I reflexively pick up my die and then, looking at a my modifiers, conclude that I might be able to succeed without rolling. I pause and ask the DM for the DC and, hearing the call, simply put my die back down and say "I take 10".

The issue you're having is that the DM is not supposed to tell you what the DC is. He can give hints, throw in any situational modifiers he likes, and you're supposed to guess if the task is possible or not considering your 'Take 10' score in the equation. Heck, you're supposed to ask the DM if Taking 10 is even possible, as mitigating factors can prevent you from doing so.

Taking 10

When your character is not being threatened or distracted, you may choose to take 10. Instead of rolling 1d20 for the skill check, calculate your result as if you had rolled a 10. For many routine tasks, taking 10 makes them automatically successful. Distractions or threats (such as combat) make it impossible for a character to take 10. In most cases, taking 10 is purely a safety measure —you know (or expect) that an average roll will succeed but fear that a poor roll might fail, so you elect to settle for the average roll (a 10). Taking 10 is especially useful in situations where a particularly high roll wouldn’t help.

Emphasis mine.

 

[pawsplay]

In some instances I've even had DMs insist that I roll regardless of circumstances that would allow taking 10. It's as if they resent my choice to not roll, to simply choose success without possibility of failure.

If they are interested in the die roll, it's because failure might be interesting, and if failure might be interesting, it's within the GM's purview to say you are not eligible to take 10.

 

[Theo R Cwithin]

The issue you're having is that the DM is not supposed to tell you what the DC is. He can give hints, throw in any situational modifiers he likes, and you're supposed to guess if the task is possible or not considering your 'Take 10' score in the equation.

This.

THere's a certain satisfaction to be had when a player says, "I'll take 10!" and the DM responds, "Very well, you take 10... and FAIL! Bwahahaha!"

Take 10 isn't there to eliminate risk from a roll.
Take 10 is there to eliminate cocky characters.

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