[Correction: I mentioned a 6,000 year old universe. The world turned exactly 6,012 years old on the morning that I wrote this (at least according to Archbishop Ussher).]
One of the things that bothers me is when people talk about "God". For example, the claim that it is impossible to disprove "God". When someone makes that claim, he or she is technically correct. This might a rather weak way to start a blog on rationalism: you can't say that "God" doesn't exist. But if you don't like it, try to show that "God" doesn't exist.
Say to some hypothetical theist that "God" has been shown to not answer prayers, at the very least not those for sick people. What response will you get? "God isn't a guinea pig. He knows that the prayers were just being used for research and therefore weren't real, so he didn't respond to them." Pick some other topic and you will get the same sort of result. It is therefore impossible to disprove "God". At any point, the goalposts that you were using can be changed.
You may have noticed my excessive use of quotation marks. I use them for an important reason. Many people seem to talk about "God" as if it is a single thing whose properties everyone pretty much agrees upon (the details may cause holy wars but they are all basically the same guy). Even nontheists talk about "God" as if it is some single, specific thing. It makes sense to me that a theist would talk about "God" because he or she is prone to only thinking about his or her god, but a nontheist has no such excuse. This idea of a single meaning simply isn't true. A sophisticated apologist's idea of "God" is completely different from the one believed in at some church down the road. Say the apologist realizes the problem of evil is actually problematic and reformulates his god so it isn't omnipotent or omniscient. This is profoundly different from the run-of-the-mill god down the street that can create a boulder so heavy he cannot lift it… and then manage to lift it. One is all powerful and all knowing, the other does not even come close. It would be silly to call these two distinct deities the same thing.
That is why you can never disprove "God", the concept is so nebulous and so easy to covertly morph should your particular version be proven false that it can never get nailed down. Essentially, the goal posts are to easy to change. As Thomas Jefferson wrote (and Mark Crislip often mentions), "Ideas must be distinct before reason can act upon them…." Before we can talk about whether these things exist or not exist, we must be clear about what we are discussing.
Instead of talking about "God" we should talk about gods or sets of gods. Unlike their nebulous cousin, these clearly specified gods can be nailed down and proven false. For example, take the set of omnipotent gods. Omnipotence leads to contradictions like the classic boulder that I mentioned above, so omnipotent gods would be logically inconsistent and could not exist. Other sets of gods get ruled out by other logical impossibilities. Then there are the gods that are ruled out by evidence. The set of all gods that created the universe 6,000 years ago has been proven to have not existent members—the universe was not created at that time. In fact, all sets of gods that created the universe at a time other than 13.7 ± 0.2 billion years ago have been shown to not exist.
The set of all possible gods is extremely large (much larger than the set of gods that humans have thought of), perhaps it is even infinite. This approach does not allow you to get rid of all gods in one go, but it provides a basis on which to deal with claims about deities. Without making the details of the gods explicit and unambiguous, you cannot have a meaningful discussion on this topic.