Atheism is the non-belief in god(s). Some people add to this simple definition and argue that atheists are actually religious by default1,2. One argument is that in order to be an atheist you have to "deny God" and by doing so, you admit that God exists. Others say that "not believing in god" is automatically a "religious" belief and that it requires "faith"1. These positions are obviously daft - most people also deny that unicorns and tooth fairies exist. But this doesn't mean that such people are members of an a-unicornist religion. They are, for various reasons, non-believers. Disbelief does not automatically equate to a religious disbelief. One articulate argument that some atheists are religious in nature was best vocalized by William James:
But however fervent someone is about things that don't exist, it doesn't make it religious. Take football. The psychology and emotionality of followers can be very intense, and we can easily imagine William James say the same thing about football fans as he does about some atheists. The truth is that 'zeal' is a trait that can be applied to any human activity where there is enough enthusiasm. You might as well say that 'religious people, psychologically speaking, have often shown a temper which is indistinguishable from football fanaticism'. In other words, just because there is a strong drive, it doesn't make it a religious drive. This is the case with the most 'fervent' atheists: their zeal does not make them religious.
Here follows the main arguments against the idea that atheism is a religion.
“Calling atheism a religion is like calling bald a hair color.”
Many apathetic atheists have simply never thought much about whether or not god(s) exist, and veer on to the side of atheism mostly by default. These atheists have not performed any conscious deliberation on theism, and have not made a religious choice. There has been no "leap of faith" into a religious stance against god. They are both non-religious and atheist.
Intrinsic atheists have never heard of god(s) and never debated their existence, and simply don't believe in them. This is lack of belief by default. For example, children don't believe in atomic theory for the same reason: they've simply never heard of it. Their lack of belief isn't religious, and their lack of belief doesn't make them a member of any religion. Likewise with intrinsic atheists: they are non-believers and are not a member of any "atheist religion".
There are already atheist religions, such as Buddhism, Daoism and Scientology. To lump all non-theists into a single "atheist religion" just doesn't make sense. There are lots of types of atheists, with lots of different beliefs. The only thing they have in common is non-belief in god(s). Therefore, there is no single "atheist religion" and there are plenty of atheists who aren't a member of any religion at all.
Religions are not defined by a single element of lack-of-belief. There are not religions to represent every non-belief. Disbelief in Santa Claus (despite not being provable) is not a "religion" based on "faith". And there isn't a religion to represent non-belief in god(s). Therefore there is no ground on which to say "atheism is a religion".
Humanism is considered by many to be the religion of non-supernaturalist atheists. But, most atheists are Humanists, therefore, not all atheists are members of a single "atheist religion".
(1902) The Varieties of Religious Experience. From the Gifford Lectures delivered at Edinburgh 1901-1902, first Edition printed 1960. Quotes from fifth edition, 1971, Collins. [Book Review]