I think the 3 answerers above me covered it pretty well. I would just add a couple points.
First, I have to quibble about the use of the word "know." Where does one draw the line between knowledge and belief? In areas of logic and mathematics, it seems like a well-defined line: I *know* that 2+2=4. But what about the real world? I can make the claim that I know that the sun will rise in the east tomorrow morning. And all the evidence shows this to be overwhelmingly likely to be true. Still, there is an *extremely* small chance that a previously-undetected black hole will swoop through our solar system and extinguish our sun before the night is over. The odds of such an event happening, even over the entire 10 billion year lifetime of our sun, are so low as to not be worth worrying about, or even considering for any practical purpose. And yet, as it is still within the realm of possibility, I can not say with absolute 100.0% certainty that the sun will rise in the east tomorrow. So do I, or do I not "know" that the sun will rise in the east tomorrow? I would argue that while the odds are not exactly 0, they are close enough to 0 that I can make the claim that "for all practical purposes, the sun will rise in the east tomorrow."
The same is true with regards to the existence of a god or gods: although, based on the evidence alone, I can not say with total 100.0% certainty that there are no gods, my assessment is that the claim of there being no gods is close enough to 100% certainty that I feel comfortable claiming that I "know" there are no gods. And although I am quite willing to have my mind changed if sound evidence for their existence is presented to me, I consider the odds of such evidence ever appearing to be so extremely low as to be not worth seriously considering.
Now that said, that is only with respect to the evidence (or lack of) for a god or gods. One can make a pretty sound case for strong/positive/gnostic atheism based on logic alone. For instance, omnipotence is logically impossible; can god make a stone so heavy that even he can't lift it? The very notion of omnipotence is self-contradicting. Other qualities of god are mutually exclusive with each other or with qualities of the universe. Omniscience (being all-knowing) can not co-exist with free will, since free will can only exist when the outcome of a particular decision can not be known in advance. If god knows in advance what you will choose to do, then that outcome is already written in stone and you are not actually "choosing" at all. Likewise, omniscience is also incompatible with the Heisenberg uncertainty principle, which established the existence of real, genuine randomness in nature and ruled out a deterministic universe that could be known in advance.
One could of course redefine god as not having these alleged properties (and really, theists have no way of _knowing_ that god has them at all), but then is the being in question really a god? Besides, moving the goalpost is not a good way for theists to win arguments anyways.
Have you read "God: The Failed Hypothesis" by Victor Stenger? He makes a pretty good case for positive/strong/gnostic atheism. Check your local library or better bookstore for it.
http://www.amazon.com/God-Failed-Hypothesis-Science-Shows/dp/1591026520/ref=sr_1_1