(First off, I'd better state that I'm using the term atheist to mean an explicit atheist, because to use it to mean implicit atheist is just plain stupid.)
There are reasonable arguements for God (most people don't know many of these) and half-decent arguements against (most people only know ones applying to the JCI God). I one thinks it through, one can reasonable go either way as to the existance of God. Theism is not necessarily an illogical position. Atheism itself is not necessarily an illogical position. Most atheists, however, arrive at their conclusion through very faulty logic and unthought-out premises.
Firstly, it's popular to assume that the JCI God is the only concept of God, or the only one worth even thinking about. The way most people sort it out, the ancient greeks were atheists because they didn't beleive in the One God.
Additionally, most people take an arguement such as the problem of evil and conclude that there is no [JCI] God, never stopping to look at the hundreds of decent responces to the problem.
Whether atheism itself is a logical position is debatable, but it's very clear that most atheists are not. They did not think through their position, yet consider themselves more intelligent and more rational than a theist who has.
Theism is not necessarily an illogical position. Atheism itself is not necessarily an illogical position. Making a claim of one's logicalness based on lack of thought is illogical.