You can't prove God doesn't exist
It is not uncommon to hear statements like, "You can't prove God doesn't exist," from apologists when they are challenged to support the claim that God exists. Such statements are an attempt to shift the burden of proof, a kind of logical fallacy.
Statements like this are based on the premise that belief in God is justified until sufficient evidence is presented to refute such existence. While this response may be considered sound under a world view which accepts the premise, this is simply a form of compartmentalization. If we were to apply that premise to all claims, we'd be unable to develop any useful picture of reality since every claim would then have to be accepted as true (until it is disproved — a burden which is especially difficult when dealing with supernatural claims).
More tellingly, though, apologists typically only apply this premise to questions that address their particular religion — and nothing else. The same Christian, for example, who argues, "You can't prove God doesn't exist," would almost certainly reject such an attempt to shift the burden of proof if it was attempted by, say, a Hindu: "You can't prove Vishnu doesn't exist!" This compartmentalization is a form of special pleading.