"...the existence of God is a scientific hypothesis like any other."
--Richard Dawkins, Evolutionary Biologist
Let's suppose that you believe termites have infested your home. You start looking around your back porch, as this is a favorite location for termites. You do not see any termites, and there is neither rot nor holes in the wood. So you check the siding of your house; same result. Not to be outsmarted by the little buggars you continue your search inside your house, checking all the walls and doors, the basement, the attic, and even your bed. But you still find no signs that termites are, in fact, taking over your home. Would it be safe to say that there are no termites in your home?
There is a common argument against this sort of investigation: "Absence of evidence is not evidence of absence." Meaning, just because you don't see something, doesn't mean it isn't there. This is a favorite for UFO abductees, bigfoot/Nessie witnesses, and theists--as if this will make their claims more believable.
In a general sense, the argument has a point, but it is incomplete. It is true that not seeing something doesn't mean anything by itself. Unless, of course, you should see something. If you have reason to believe that if something exists it would manifest in some way, then not seeing a manifestation decreases the probability that it exists. As with the termites, if you look thoroughly and see no signs of an infestation, then the odds are that there are no termites. Furthermore, the more extensively the search is conducted, the more places you look, and the more time you spend looking, the less likely you are to find something affirmative in the places you have not yet looked. If you look over 50% of your house, there is still a pretty good chance that termites might be in the remaining 50%. But if you look over 95% of your house and find not a single trace of termites, it becomes unlikely that you will find anything in the remaining 5%.
Now, there is a chance that you may have over looked parts of the house, or failed to notice something. This is a possibility, but still, as you continue to look and see nothing, the odds of finding termites continues to drop. At this point would you be reasonable to believe your house is infested with termites? No.
Let's change the scenario slightly. Let's say an exterminator knocks on your door, claims you need his services, yet finds absolutely no evidence of termites, would it be reasonable to pay him to spray your house? No.
As with claims of mythical creatures, as more studies and searches are conducted, the absence of evidence, at the very least, implies evidence of absence. In the case of god, such searches have been going on for hundreds, even thousands of years, and still we see no conclusive evidence that a god exists. Indeed, it is more reasonable to believe in UFO's, Bigfoot, Nessie and the Flying Spaghetti Monster than an unsubstantiated god claim which has been around since the Bronze Age.
Some might refute this line of reasoning with a proclamation that the god they believe in doesn't manifest because it is timeless and immaterial. Ok, let's look at this a different way. Based on this claim, there are three different possible types of gods: a god that exists and manifests, a god that exists and doesn't manifest, or a god that doesn't exist. Tell me, how do you tell the difference between a god that exists and doesn't manifest, from a god that doesn't exist? If a god doesn't manifest, whether it exists or not, then it is inert, and, therefore, useless. If it does manifest, we are back to looking for such manifestations, and basing our beliefs on the evidence we do find. If a god exists we should expect to find evidence supporting that; if we don't find evidence, then there is probably no god.