Supernatural explanations are no explanation at all.
I think it intellectually dishonest, the way some people take a Big Question, and pretend to provide an answer to it through religion. For that is all it is. Pretending. If you dig a little deeper into the so-called 'solution', it turns out to be little more than a dressed up admission of ignorance. Surely it would be better to just cut to the chase and admit ignorance right from the start, thus avoiding all the superfluous (and sometimes downright harmful) window dressing.
Lest I be accused of floundering in baseless generalities, I want to focus on three particular examples of this rhetorical masquerade: origins, meaning, and morality. These are (in my experience) perhaps the most common arguments people appeal to in order to justify their belief in a deity.
Where did the universe come from? It's a tough question, and I haven't a clue what the answer is. Some religious people think that positing a supernatural creator (i.e. God) provides the answer. But surely it is clear that this achieves nothing - it merely pushes the question back a step, so that we must ask "where did God come from?". He is usually conceived of as being eternal, but why not skip over him altogether and just apply that very same answer to the natural universe? As Raymond Bradley put it: "I find only fallacious inference in the supposition that we can explain why anything at all exists by hypothesizing that something else exists in addition; for that supposition starts one on the path of infinite regress."
Questions of meaning & purpose are other favourites of the religious. But again, so far as I can tell, it amounts to nothing more than pushing the problem back one step. They say that without God, our lives have no (ultimate) meaning or purpose, and that God provides that purpose. But how exactly is that supposed to work? After all, what is the meaning of God's existence? If God has no ultimate meaning (and it is difficult to see how he could), then clearly he cannot pass it on to us. But if you want to stipulate that he does have an 'ultimate meaning', then what does that achieve? Could you not (once again) just skip out this pointless intermediate step, and simply apply the stipulated meaning directly to human existence?
I think part of the appeal here is the desire for your life to be part of something bigger than yourself. But, of course, religion has no monopoly on meta-personal goals. Any sort of mass movement (e.g. political or social movements) has this very same property. So how is being a Christian any more meaningful than being a Communist? One presumably ends up appealing to the special 'meaning' provided by God, which brings up those problems discussed in the previous paragraph.
Morality is a closely related matter. Some suppose that without God, there is no reason why you really ought to do one thing rather than another. But how does adding God into the equation help things here? (Short answer: it doesn't!) Suppose God wants you to do X. Why should you do what God commands? Surely this is just as troubling a question as the original "why should you do X?" was? Even supposing that a benevolent God exists, one must still face the old Euthyphro dilemma: "Is X good because God commands it, or does God command it because it is good?" We must surely choose the latter, but this demonstrates that God is superfluous to morality, which exists (or not) quite independently of God.
I'm sure you can see the general pattern here: We have an unexplained problem. The religious suggest that God can explain this problem. What they fail to realise is that the concept of God has at least as many problems of its own. Whatever we didn't understand about the universe, we still don't understand about God!
So, I must conclude, the explanatory usefulness of God is nil.
Disclaimer: I do not here make any claims about whether God does or does not exist. [Of course he cannot be 'disproved', any more than you can disprove that there is an invisible intangible dragon in my garage. Though I do think there is precious little reason to believe either!] I am merely drawing attention to the fact that positing his existence does not serve to explain anything (or at least, not those 3 things discussed above).
A 'God of the gaps' is inevitably full of gaps himself. I find it remarkable how rare it is for people to acknowledge this fact.