Many discussions end with the statement "you can't prove a negative". This is, of course, silly. I've heard it even from people who are quite expert at physics. People who should know better
Proofs of impossibility abound in mathematics and logic. Reductio ad absurdum is typically the first kind of proof learned when studying such things, and this really is nothing more than assuming the opposite of what one wants to prove, and showing that this cannot be - proving a negative.
I suppose what most people mean by it is that in an open system, such as the universe, which is not constrained by any rules (at least none we are aware of), it is impossible to prove that something does not exist. Showing that no one has ever seen a unicorn is not proof that one won't come down from the stars and eat your cabbages tomorrow.
The problem with this is that in such open systems, it is impossible to prove anything at all, negative or positive. No matter how many times you drop a ball and observe it falling downwards, that still is not proof that it always happens. It is still possible that the next time you try it, the ball will fly up to the ceiling and stay there. Not terribly probable, but also not impossible - at least not provably so. This is why we only have theories in physics, not theorems.
So why am I saying this? Am I arguing that because we can't prove anything, there must be a god? Of course not, don't be silly! I just want to do my bit to improve the argument a bit.
As everyone knows, a theory in physics doesn't mean a guess. But it is still one notch below theorem on the scale of knowledge. Theorems are theories that have been proven, but unfortunately we can only get those in closed, rigid systems such as mathematics (and even there we can't trust them completely, as Gödel showed), but theories are of course still useful. We assign probabilities to hypotheses, based on how well our physical, empirical experiences confirm them, and when the probability exceeds a certain (non-determined) value, we call the hypothesis a theory. I know there is a bit more to the process than that, a theory has to predict previously unobserved phenomena to be considered useful, but basically that is it. The probability has to be high enough to be considered a theory, but it can never be proven.
If the probability climbs high enough we start talking about law instead of theory, but even then it is not a proof (most evident from the fact that everything in physics we call laws were shown in the 20th century to be flat out wrong - but very useful approximations)
So it's not useful to talk about not being able to either prove or disprove god's existence, since we can't prove or disprove anything at all. We can however assign it probabilities based on empirical evidence.
Like Dawkins, I think p(god) is quite close to 0