Here's a Wiki list of seven empirical arguments against the existence of God, along with seven lines of response.
1. The argument from inconsistent revelations contests the existence of the deity called God as described in scriptures — such as the Jewish Tanakh, the Christian Bible, the Muslim Qur'an or the Baha'i Aqdas — by identifying apparent contradictions between different scriptures, within a single scripture, or between scripture and known facts. To be effective this argument requires the other side to hold that its scriptural record is inerrant, or at least to assert that a proper understanding of scripture gives rise to knowledge of God's existence.
Refutation: God's existence has no necessary connection with Scriptures, or, for that matter, any human conception of God.
Secondly, just because you have nine counterfeit $100 bills in your hand does not mean that the 10th is also counterfeit. There may or may not be a genuine revelation that points accurately to God.
Thirdly, if God does have a Scripture, it need not be inerrant to serve its intended purpose -- just like a One Way sign can be pock-marked, dented, and rusted and yet still clearly serve its purpose.
2. The problem of evil contests the existence of a god who is both omnipotent and omnibenevolent by arguing that such a god should not permit the existence of evil or suffering. The theist responses are called theodicies.
Refutation: Cancer bites. Death bites. Poverty bites. Suffering unjustly bites. Evil is not just a perception; it is real. The problem of evil is addressed in the Christian Scriptures from Genesis to in the book of Revelation. We are assured that it exists only temporally, and will be defeated in time.
Secondly, without God as Creator and Law-giver, evil is an incomprehensible, meaningless idea. There can be no evil where there is no good. There can be no good vs. evil where there is no "ought". An amoral atheistic universe does not contain an "ought" as part of the furniture of reality. We thus find in this argument from evil atheists arguing using assumptions which are only authentic if theism is true.
3. The destiny of the unevangelized, by which persons who have never even heard of a particular revelation might be harshly punished for not following its dictates.
Refutation: Adequately covered in the book of Romans. God judges each man and woman according to their hearts and consciences. The sacrifice of Christ covers the sins of the whole world. God will be just in his punishments and rewards.
The bigger problem is why man should think that life ought to be just at all. Once again, this is a conception which must presuppose theism to be an authentic issue.
4. The argument from poor design contests the idea that God created life on the basis that life-forms, including humans, seem to exhibit poor design.
Refutation: Once again this is reading-into the definition of God what we think God should be and do. This argument is linked to the problem of evil -- the universe is not the way we imagine a perfect universe should be. But this leads to another question -- why should human beings be wired with this deep conception of the ideal, or Perfect (and, an "Ought")? Like other abstracts, these abstracts point to a perfect world, which the Scripture assures us shall be accomplished in Christ. And, like other abstracts, they show that atheists when they argue do so on the basis of presuppositions about reality that are only authentic assuming theism is true. If atheism is true, not only should things not make perfect sense, they should make no sense whatsoever -- because the very fabric of reality is, under atheism, senseless, and sense-making human beings an absurd anomaly.
A bigger problem is also why an unplanned, unguided, uncreated universe should exhibit any evidences of design whatsoever.
5. The argument from nonbelief contests the existence of an omnipotent God who wants humans to believe in him by arguing that such a god would do a better job of gathering believers.
Refutation: Same fallacy as the other arguments that argue, "if we were God, we wouldn't do things this way". That's a losing argument for reasons cited. God has entrusted the saving word of salvation into the hands of ordinary men and women. And he is using them to propagate his message. It is interesting that in Revelation it says that the gospel shall be preached throughout the world -- this at a time when the Christians were a small, insignificant, beleaguered sect. That statement has been fulfilled.
6. The argument from parsimony (using Occam's Razor) contends that since natural (non-supernatural) theories adequately explain the development of religion and belief in gods, the actual existence of such supernatural agents is superfluous and may be dismissed unless otherwise proven to be required to explain the phenomenon.
Refutation: Occam's Razor is a mere heuristic. One ought not stake one's eternal destiny on a mere heuristic. And it fails in this case because everything requires not just an explanation for its existence but a sufficient reason and cause, and the only sufficient cause for an elegant universe in which morality and rationality are not just subjective feelings or apprehensions but part of the very fabric of existence, is a Creator who is himself both personal and moral.
7. The analogy of Russell's teapot argues that the burden of proof for the existence of God lies with the theist rather than the atheist.
Refutation: Russell's teapot is just the flying Spaghetti monster of old. Refuted here. Such arguments merely point out the desperation of atheism which finds itself resorting to ridiculous caricatures.
An orbiting teapot, unlike God, has no explanatory power.
All things whose existence is contingent, i.e., not necessary, require a sufficient reason or cause for their existence. God provides a complete, full, and satisfactory explanation for the existence of the universe. The floating teapot explains precisely nothing.
In addition, the idea of God resonates in the human heart in a way that teapots and spaghetti monsters do not. Indeed, belief in God may be properly viewed as basic, as Alvin Plantinga has suggested.
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The problem with empirical arguments is God is an immaterial Spirit who exists apart from his empirical Creation. Trying to disprove God from empirical evidence cannot succeed -- but neither can trying to prove God from empirical evidence succeed, beyond probabilities which will be dismissed by those wishing to do so. So, no one is going to win this argument, and it comes down to, at the end of the day, the disposition of one's heart.
God has set sufficient evidence in place to make his existence apparent; it is the condition of our hard, bent hearts that resists the knowledge of God. Free-will, contrary to the assertions of strong materialists, is real. It is real because God wants those who will spend eternity with him to freely choose him. For this to be the case, not choosing him must also be a real option. For this ability, atheists can thank God -- they owe a lot to Him.
List of Arguments from Wiki.