Originally, this thread was about the question of whether it is possible to prove a universal negative. I still believe the answer is yes, but of course the claim has to be stated unambiguously. The reason we can prove, for example, that there are no positive whole numbers n, x, y and z such that n>3 and x^n+y^n=z^n is because we know quite specifically what we mean by numbers, powers, addition and equality.
This does present some problem when trying to apply these ideas to the question of existence of supernatural beings or gods of any kind. What exactly do we mean by "god" anyway?
The usually description of the Christian god is actually rather specific. It is specific enough for me to be confident that the vast majority of evidence points to the likelihood that this god does not exist but is only the creation of human imagination.
But, if we open up the question to "some sort of god" without being any more specific, then it becomes so vague that I don't see how we can say anything meaningful about its (non)existence...or the significance of whether such a thing exists.
Commonly for Deists (and for Nick above), there seems to be an assumption that if some conscious being created our universe, then that thing is "God". But, that isn't so clear to me.
Suppose we eventually found out that our universe was created by a scientist in some other universe with very different laws of physics. Suppose this scientist works for a government that gave him a large amount of what they consider money to develop a method of generating lots of energy, and his idea was to build a machine that created a universe filled with "stars" that turn hydrogen into helium through a fusion process and another machine to collect that energy (through the things we call "black holes") for use in his universe. Suppose he did not even realize that life would develop in this universe (since the laws of physics in his universe are so different and he thought that only THOSE laws were sufficient for life)...so we're just an accident.
This is really just science fiction. I'm not claiming I believe this story, only that I can imagine this story. Actually, I can imagine this story being true more easily than I can convince myself to believe in any of the more traditional creation myths of religions on Earth, but that's beside the point.
The point is, would we consider this extra-universal scientist to be "God" merely because he created ours? I think not. Several things are missing.
One important thing is that he doesn't really care about us. That, at least in my meaning of the word, is an important part of what would make something "God". Already, if the creator of the universe is something that doesn't care about us, then I'm less inclined to use the word "God" to describe it.
In this case also there does not seem to be anything "supernatural" going on. For certain my science fiction story speculates about another universe where the laws of physics are different, but this is not so much SUPER-natural as "an alternative nature". (Some of our own scientists have speculated about the use of String Theory to allow us to create tiny universes in our own particle accelerators. If we did create a tiny universe with different laws than ours in this way, would we become super-natural beings ourselves? Arguably, we would be to anything living in there...but then this seriously weakens the meaning of "supernatural", doesn't it?)
Moreover, and I think this is important too, there is something missing here as far as MORALITY goes. Even Deists (like Jefferson) refer to their god as the source of morality. But, this scientist in the other universe may not be a moral example (perhaps he sabotaged the career of the scientist in the lab next to his to advance his own, and perhaps he beats his children...we don't know) nor does his action necessarily have any moral implications for us, the inhabitants of his creation.
Finally, this scientist who created our universe does not necessarily possess either omniscience or omnipotence. Having the power to create the universe is certainly impressive, but it doesn't necessarily mean that he knows everything or can do anything.
In conclusion, let me repeat that I do not believe the universe was created by a child beating, money seeking scientist from another universe. I'm just using this as an example to illustrate my point:
Those who argue that "there must be a god because SOMETHING created the universe" have to explain to me what the word "god" means to them, because the universe could have been created by something I would not want to describe as "god".
(Also, they have to explain to me how they know that something sentient created the universe as opposed to the many alternatives I can imagine there as well...but that's another story!)