Here's some classical rational arguments for God by Aquinas, Anselm, Descartes, Pascal, Lewis, and James, using my own paraphrasing of them to make them short. I think Pascal's and James' are probably the ones that will interest atheists the most, as the others, while interesting, are rational arguments *for* the existence of God, but these pragmatic arguments say that it is rational *to believe* in God. An important difference. (Most people confuse Pascal's wager as an argument in the first case, not the second, as it was intended -- he wrote it for Christians, not trying to convince atheists.)
Everything in science has a cause. What caused the big bang? If you say nothing, that is a less scientific statement than saying something. Therefore, rationally, something caused the universe. Since that something must stand outside of time, the only thing which fits our concept of a powerful entity sitting outside of time is God. Though you could posit something else that fits those shoes, like an omnipotent 8th grader in a higher dimension creating our universe as a science fair project, whatever it is will resemble God to some degree.
Note: The universe cannot be infinitely old. If the universe started an infinite amount of time ago, we could not get to the present one second at a time.
Unlike with unicorns and fairies, we know that God has to exist simply from the definition of him as the most perfect being, as existence is one of the required attributes for perfection. Certainly a god that exists is more perfect than a god that doesn't exist.
3) Descartes (heavily adapted):
God or evolution made us (or maybe space aliens). Therefore, we were made either with a purpose, or survived by being be more fit than other species, with useful traits retained and harmful ones pruned. All humans have a yearning for God, hence atheists' greater belief in the supernatural than theists, as they attempt to fill their need another way. But this need makes no sense in any creation method (unless we were made by aliens, I guess, who wanted religious slaves to tend their stargates...) unless there was a God. A creature who has blinded or deceptive senses is useless evolutionary, and wouldn't be done by a kind and loving God. Therefore, since in both cases we are given facilities which we should be able to trust, the yearning for God should be seen as actual evidence that God does exist.
We don't know if God exists or not. However, we *do* know what the consequences of belief and nonbelief are. When dealing with uncertainty, the rule is to ignore the non-quantifiable probabilities and focus on the consequences in order to make a rational decision. In this case, it is a very simple decision, as with even a small (but non-zero!) chance of God's existence, the rational decision is to believe.
Note: this means that if you think there's a 0% chance that God exists, you shouldn't believe in him. In any event, trying to believe in something that you think is completely false is stupid, and probably impossible to boot.
However, it does mean that if someone thinks that there is a chance that God exists, that you shouldn't criticize them for being irrational, as well.
The historical record, unlike with Mormonism and some other records, shows that there probably was a guy named Jesus who ran around on earth and did stuff in front of a bunch of people. There's several possibilities: 1) Jesus was a man, but a great moral teacher (Christian "modernism"), 2) Jesus thought he was the son of God -- but was just kind of crazy, 3) Jesus was a sort of crazy evil cult leader guy, like David Koresh, or 4) He was the son of God. Lewis eliminates the first three possibilities due to various things like his disciples almost universally dying for him (sorry, I'm running out of time here, I have to take off for Jiu-Jitsu), and so concludes that Jesus must have been the son of God.
6) James (the Will to Believe, one of the greatest works of philosophy: http://falcon.jmu.edu/~omearawm/ph101willtobelieve.html)
We don't know if God is real or not. However, we must choose -- we cannot put it off. As long as the option is a live option (in other words, it's an option a specific person could actually believe in, as opposed to "the world was created by My Little Ponies") which is rational and not self-contradictory, then let him believe it without shame. The person who tediously insists on 100% proof of anything will be sorely disappointed in life (and probably a bore, to boot), since even science doesn't give us things that are 100% true. A tedious skeptic is just as bad, if not worse, than a fatuous believer.
Imagine a person put a gun to your head (i.e., it's a forced decision), and says that you have to decide, right now, if P=NP or not, and how you pick will govern the rest of your life somehow. It's a momentous, forced, live decision (as either P=NP or P!=NP could be true), but you *must* pick, without firm proof either way. James' point is that in such situation we can freely choose either, without shame, or without being called irrational.
So there you have it -- four rational arguments for the existence of God, and two that the belief in God is rational.