The Christian is challenged to explain the universe or the apparent design in life. They say that God created it, but then the atheist responds, “But who created God?”
Christian response #1
The most popular Christian response is probably to attempt to invalidate the question by saying that God is uncreated by definition.

The answer is that [“Who created God?”] does not even make sense. It is like asking, “What does blue smell like?” Blue is not in the category of things that have a smell, so the question itself is flawed. In the same way, God is not in the category of things that are created or caused. God is uncaused and uncreated—He simply exists. (Source)
God by definition is the uncreated creator of the universe, so the question “Who created God?” is illogical, just like “To whom is the bachelor married?” (Source)

So have we somehow used a definition to create God? Or at least argue for his existence? Hold that thought, because that reminds me of a joke.

It seems that there was a dairy farmer with a large herd who wanted to improve milk production. He contacted the local university, and they assigned three professors to the project. After a month, they presented their work.

The psychologist showed how changing the wall color inside the milking parlor and playing soothing music relaxed the cows and improved milk production.

The mechanical engineer suggested improved pumps on the milking machines. Quicker turnaround meant more time eating in the fields.

The physicist was the final expert. He went to the blackboard, picked up some chalk, and drew a large circle. “Consider a spherical cow entirely filled with milk.”

Your reaction to the physicist is my reaction to the two quotes above. Sure, we can define God as “the uncreated creator of the universe,” but if that definition is supposed to be an argument for this God, then you’re as disconnected from reality as the physicist.
Don’t pretend that you can sit back with your arms crossed as if you’ve justified your position in any way. Your religion may say that God was uncreated, but that is no answer in the real world. If “Who created God?” exposes an unsupported part of your argument, then come back after you have justified the claim that God was uncreated. Make it a conclusion, not a presupposition.
Before you say that the Bible confirms that God is eternal (for example, “The hope of eternal life, which God . . . promised before the beginning of time,” Titus 1:2), remember that “the Bible says so” is theology, not evidence.
Response #2
Here’s an interesting angle:

As a logical refutation against God as creator and designer of the universe, the who created God question completely misrepresents philosophy of science. This is because, in order to recognize an explanation as the best, you do not have to be able to explain the explanation. In order to say that A caused B, you do not have to be able to explain where A came from. (Source)

So what are you saying? Are you admitting that you can’t explain where A (God) came from? If the ordinary questions (“Where did it come from?” or “How long has it been around?”) can’t be answered in an ordinary way, you don’t just assert that; you give evidence to justify it.
The typical response at this point is to argue that God is the unmoved First Mover or the necessary being required to create the first contingent being, but these philosophical approaches aren’t useful at the frontier of science. Science does have questions about the origin of the universe, but it has also answered many questions. Religion, by contrast, has taught us nothing about science.
Let’s return to that last source.

In order to say that A caused B, you do not have to be able to explain where A came from. For example if we came across a pit of ashes in a field, we would be justified in inferring that there was a fire, even if we had no idea whatsoever where the fire came from or what caused it.

Answer 1: Instead of a fire, I’d prefer to explain the ashes by a wizard. You’ll say, “But where did the wizard come from?” Sorry, that question is out of bounds and can’t be used to cast doubt on my explanation. Remember that you don’t need the explanation of the explanation.
Answer 2: I’ll accept fire as a reasonable explanation for ashes because fire is common and we know it creates ashes. Now tell me why I should find God’s actions in the world as familiar as those of fire.
Fires are common and unsurprising, but there is no good evidence for a supernatural anything (in particular, creators of universes). See the difference? Don’t draw a parallel between something common (fire) and something so uncommonly uncommon as to be nonexistent (God).
Response #3
A final response attempts to shore up the claim that God was uncreated. One Christian blog responded by saying that everyone says that the ultimate cause was uncaused and that if this challenge knocks down the Christian worldview, it knocks them all down. Atheists are living in glass houses when they demand justification for an uncaused beginning.
The problem, of course, is that there is no scientific consensus about the origin of the universe that says that it was uncaused. And when there is a consensus, it will be based on evidence.
Unlike how Christianity makes its conclusions about the questions of nature.
(See also: “How Does the Kalam Cosmological Argument Suck? Let Me Count the Ways.”)

Science continues to replace
God-filled gaps in our understanding
with all-natural ingredients.
And since we don’t need God
to explain the existence of the nature of the universe,
 we don’t need God, period.
— Mitch Stokes, paraphrasing an atheist argument

Image credit: Tim Green, flickr, CC