Police commonly ask this question to obtain an admission. The fact of the matter is that no-one actually knows the exact speed of the car -- speedometers and radar guns alike have margins of error. Of course once you admit to going a certain speed, that is a legal admission that can be used as proof that you were actually going a certain speed.
Over the years, the driving population became quite savvy to this not-so-nice little trick. Driver's would commonly answer this question with a curt "No."
The latest twist in this rather childish and 1984-esque battle of words involves Police using the drivers answer that he does not know how fast he was going to add another charge in addition to speeding: careless driving. It does, in a way, make sense, the driver was not only speeding, but didn't even know how fast he was going.
Our advice is to answer the question, but not admit a number.
One commentator has suggested that "Somehow, I have a feeling that you are about to tell me," delivered with a sheepish grin might break the ice and end the "battle of words."
From a straight legal perspective, our advice is to say, "Yes." This will usually be followed up a more direct attempt to obtain an admission, something along the lines of "How fast were you going?" A direct answer might be called for at this point - you could try the above idea, or simply inform that officer that you aren't answering.
"With respect Officer, I'm not answering that." is a perfectly reasonable response to the police trying to get you to hang yourself with an admission. You know it, and they know it too.