Here is a set of arguments of why one might be an atheist. The first and third of these need not be applied to just atheism, if one can satisfy one's self as to the validity of a religion through them.
1: What else should I be?
The simplest way to get to atheism is to not believe any claims of existence of any god. Going into the details on this gets sticky and offensive, hence I have trimmed it. Anyway, I am pretty sure that people can come up with some pretty good reasons if they try (even believers can - the thing is that they can overcome this with simple faith. Faith can be powerful and legitimate... but it cannot come by intent. If you do not have it, continue!). If one does not accept claims of deity-existence, one is in agnosticism. What from there? Now that we have scientific bases for the workings of the world * , one can apply Occam's Razor to get the simplest working hypothesis - scientific atheism. I hardly need say 'scientific'. Atheism hardly exists without science to provide an alternative. In the distant past, science couldn't explain jack, when it existed at all. Thus, it wasn't even a candidate in Occam's Razor. Some religion or another won by default. Now, it contains at least one fewer entity and underlying principle than any conceivable religion that fits observations, so as long as the world does not seem implausible from a scientific perspective, it comes out on top.
* This is not to say that science knows how the world works. However, the method provides a viable framework other than faith which can be used to understand the world.
2: Contradiction between Religions
The contradictions between various religions are obvious. If one of them is right, this usually makes most of or all of the others wrong. If a religion relies on revelation, then its argument is weakened if it must admit that revelation can be wrong, and in fact usually is! Most religions will ignore this, discounting the revelatory origin of other religions. But it's there anyway - If a religion's explanation for other religions doesn't jibe with what the other religion's history is, we regress to the original question of who to believe.
Taking it from another angle, if you find yourself equally convinced of a wide variety of options, you don't know. Thus you are agnostic. As above, agnosticism may lead to atheism.
On the other hand, if you are in this position, Atheism may not be the right direction to be going. You may wish to check out various versions of
Unitarianism. I have heard that
Ba'ha'i also has a good way of dealing with this, though I haven't spoken with any members.
3: Where's the sense?
Here I take a wholly different tack. Suppose that there is exactly one omnipotent god. God's motives are not clear, given what we see about us, in terms of strife and destruction, starvation, etc. (if they are clear to you, /msg me, please!). Now, it is possible to accept the existence of a divine being whose motives cannot be understood. Many people do. Those of us who cannot bring ourselves to accept that possibility must either assume either that there is some potentially understandable reason out there that we haven't figured out yet, or there is no one reason. The latter is virtually a denial of monotheism (though not entirely...). The former is fertile ground for fantasy writers, especially humorous fantasy. However, it's not a great way to live.
This fits well with the famous verse, including: "God is not good, or God is not god" (who wrote that? I know that's not all of it). If God expects and requires us to worship it for carrying out an agenda we can't understand, even if the agenda is a good one, then god is not good. I can understand if God wishes we worshipped, but if God is good and realizes it is operating under incomprehensible motives, then we aren't required. That may not seem like atheism, and it isn't. But if you are an agnostic heading towards atheism, it's helpful to get rid of fears. On the other hand, someone who is going out of their way to be afraid will probably invent a lot more possibilities to be afraid of (I do, but I don't lose sleep at night over it).
Working one's way out of a polytheism is much more difficult since gods can work at cross purposes and are usually of limited power. You lose the third argument altogether.
These are the reasons I can think of. There are no doubt more arguments, and probably better statements of those made here.