There are two major arguments in the world today for God. Many people give many reasons to believe in God, but they do not generally provide an argument for whether or not there is a God; people would rather give reasons for why they would like there to be a God. The only two arguments which get vaguely close to being real arguments for God's existence are the Cosmological Argument (also known as the First Cause Argument) and the Teleological Argument (also known as the Argument from Design). I'll just address the Cosmological Argument for today.
Thomas of Aquinas is the most often quoted on the Cosmological Argument. The question, which gets thrown around rather like an infallible weapon that will silence any atheist, is generally phrased as "How did everything get here?" or "Why is there something rather than nothing?" These are basically the same question, but for the sake of clarity I shall respond to the second, as it is worded simply and efficiently and lessens the chance of misunderstanding.
The Christian answers the First Cause question by postulating that a supernatural being, which existed independently of the natural universe, created everything which is scientifically observable. Now, we must first ask where God came from, and why he is exempt from the law of everything needing a cause. The Christian explains that God, existing independently of this universe, is not constrained by such natural forces as time. So an essential component of the Christian's argument is the idea that anything existing outside the natural laws we observe today (which is the definition of supernatural) does not need a cause. Now, it is a well-known fact (articulated wonderfully by Stephen Hawking in his latest book, The Grand Design) that the natural laws we observe today did not exist at the beginning of the universe. They do not even function as we perceive them today. Our brains see time as a straight line, extending in both directions. We assume, then, that the line must have a point where it began and a point where it ends. This is, however, completely a construct of our own consciousness. Time- if we were to give it a spatial property such as we do when we think of it as a line- is rather like a sphere. Things do not begin and end in the way we tend to think they do. In that same manner, the universe did not have a 'beginning' in the way we assume it must have. It was not a specific point on a line that we call time- it was more like the North Pole on a globe. We can think of the beginning of the universe as the North Pole and the end as the South Pole- we can continue to move north, but once we get there, we cannot move any further north. It does not exist. So this idea of everything needing a beginning is resting on a constraint of our own perception- time itself has no beginning. It is like a sphere- it has no point where it begins or ends. We can say that, in a sense, the universe is eternal. Within the concept of time, it is wholly without beginning or end.
Now, a Christian may still argue that even if time does not have a beginning or end, it must have been brought into existence by something. Ah- so even something that is not constrained by a beginning or end still needs a cause? Well, if we make that assertion, then the theistic god must be brought to trial. If even timeless entities must have a cause, then we would be forced to conclude, as so many have done in the past, "It's turtles all the way down!" Theists have a choice; either they say that eternal entities are not subject to the law of causation- which means we then are perfectly warranted in the conclusion that this eternal universe is all there is- or they can say that even eternal entities must have a cause, which means their God is thrown into the same boat as our universe.
What if we were to conclude that entities outside of time must have a cause as well? In that case, it seems impossible that we are here at all. It is absolutely impossible in theory for anything to exist, yet here we are. Let me respond to this question with another question: what is nothing? We should take a minute to pause and think about the actual definition of that word, "Nothing." What would things be like, let's ask ourselves, if there was nothing? Well, we've got a problem: that is an impossible question to answer, even in theory. Because "nothing" being used to describe anything, even a lack of anything, is nonsensical. Nothing is exactly what it sounds like: absolutely nothing. Not a vacuum, or a lack of existence of any sort, but rather just a word to describe something that does not exist. That is why, in a rather confusing mind-bender, is why there is something: because "nothing" does not exist. By its own definition, it does not exist. We are left with only one alternative: existence. What exactly does exist is a question for science, but for the philosophers, we can confidently answer this question: It is not impossible for something to exist. It's impossible for nothing to exist.
Now, that's a rather heartening thought for atheists, isn't it? No matter what happens, there will always be something. There always has been, and always will be, existence.