Occasionally an atheist or skeptic will tell me, after countless rounds of argumentation, that I still haven't provided so much as a "shred of evidence" that God exists. At that point I usually leave off my part in the discussion, knowing that I have more than met my responsibility as a Christian witness. I post this only to remind Christian apologists (me included) that we are charged to be wise with our use of time and energy:
As Christians, we believe that God is quite capable of revealing himself to humanity. Moreover we maintain that he has actually done so, through various forms of evidence.* These include the precise fine-tuning of the universe for life, the specifiable complexity of living organisms, universal human awareness of moral responsibility, the prophetic history of Israel, religious experience, and of course the miraculous ministry, crucifixion and Resurrection of Jesus Christ. Atheists, on the other hand, often argue that God is not only unknowable, but scientifically undefined and therefore meaningless. Since there is purportedly "no evidence" for God in principle – when "evidence" is narrowly defined as verifiable sightings or scientific detection of God himself, rather than some sort of supporting data or argument – the existence of God is unknowable in principle. This all leads to some rather fruitless discourse.
If for example I present the bacterial flagellum or the mammalian eye as evidence of intentionally designed complexity, the argument is rejected by atheists because we cannot actually detect the designer himself with scientific instruments, and therefore functional complexity that exceeds the greatest human engineering marvels by many orders of magnitude is not evidence for the existence of God. If I cite abundant historical evidence to the effect that Jesus existed, that he predicted his own death and resurrection, and then appeared to believers and critics alike (think Paul and Thomas here), then atheists reject this as well on the grounds that resurrections are only possible if we already know that God or the supernatural exists – so the argument is "circular."
In other words, by an implied positivist epistemic standard, God should be visible, measurable, or otherwise ever-verifiable scientifically, or else he should be presumed nonexistent. This situation seems to have arisen largely not only from reliance on a now-defunct philosophical movement (logical positivism) but from a misunderstanding of what constitutes "burden of proof." The idea basically is that anyone claiming to hold a rationally warranted or evidentially supported belief in God has to prove it to the satisfaction of atheists, who can always opt to simply fold their arms, chuckle condescendingly, and say, "That's not evidence. Where's the evidence?" There seems to be some duplicity at work here. For example, while any and all critics of macroevolution or universal common ancestry are said to be guilty of purely subjective personal incredulity or a dangerous denialism (quite regardless of their arguments), atheists who summarily dismiss all the evidence mentioned previously by muttering something about Santa Claus or the Flying Spaghetti Monster are said to exhibit coolheaded rationality and a healthy, open-minded skepticism. Such a double standard is, naturally, evidence of deep bias.
Given that I don't happen to believe that all of reality is scientifically verifiable (history, the origin of the universe, the validity of logic, and memories of what I did last week are not subject to empirical verification), I will happily concede that God does not often appear to lend himself to researchers for the sake of scientific investigation. However, even where God has evidently gone out of his way to make himself visible, as during the ministry of Christ on earth, atheists often object that God by definition is not empirically investigable! Christ is reported by early Christians and rabbinical Jews alike to have performed seemingly miraculous "signs" (though the rabbis attributed these to sorcery) but these are not valid evidence, I've been told – because they can only be valid if God exists, and to say God exists just because some person does "magic tricks" only begs the question.
In short, there is no way to meet an irrational demand for evidence that is at once natural and supernatural, verifiable and unverifiable. Any ongoing attempt to satisfy such a demand is a waste of everyone's time, and I happen to think that mine is particularly important.
* "Evidence" here means basically any form of observable data or valid argument which "confirms" a hypothesis H by making it more probable than it would be given only background knowledge K relevant to that hypothesis. So if Pr(H/E & K) > Pr(H/K), E is evidence for H.