When a religious believer asks an atheist, "Do you believe that God does not exist?" it is imperative that we pause for a moment to clarify something: Which god? Are we being asked whether we believe some particular god does not exist, or are we being asked whether we believe no gods of any sort exist? The answer might or might not be different. It is even more important to recognize that we are being led into a trap, or at least something the religious believer almost certainly regards as a trap.
My answer to both the broad question (i.e., "Do you believe that gods do not exist?") and the narrow question (i.e., "Do you believe that my preferred god does not exist?") is the same: No. I do not believe that gods do not exist, and I do not believe that your preferred god does not exist. And yet, I don't believe in any gods, including your preferred god(s). That is to say, I don't have any god belief. But what does that mean? It means I live my life as if gods probably do not exist, but I am not terribly interested in claiming that they do not exist, have never existed, or could never exist at some unspecified point in the future. Perhaps they've been here all along but chosen not to reveal themselves and will someday do so.
You see, what the religious believer is trying to do here is shift the burden of proof away from them (which is where it belongs) and on to you. They are doing that by trying to get you to make the sort of positive assertion that might require evidence to be justified (e.g., "I am 100% certain that your preferred god does not exist."). If you were to say that you believe no gods exist, then they will demand you present your evidence in support of this belief, etc. But they are the ones claiming god(s) exist, and so the burden of proof is theirs alone.
As an atheist, I don't believe in gods. As an agnostic atheist, I not only don't believe in gods, but I make no claim to know with certainty whether gods exist. But isn't this a cop-out? I don't see it that way. I'm open-minded enough that I'd quickly believe in gods if religious believers met their burden of proof by providing sufficient evidence to support their claim. But until that happens, the only rational course of action is to live my life as if gods probably do not exist.
Of course, I am only one atheist describing the approach I typically take. Other atheists handle questions like this in different ways. For an example of a different approach that also works well, check out this post by Herald Newman at The Truth Seeking Atheist.
