The Abrahamic (or Judeo-Christian) concept of "god" is a logical impossibility on many levels. The powers attributed to such an entity — most commonly omnipotence, omniscience, omnipresence, and absolute benevolence — contradict each other, and make its existence highly questionable, if not outright absurd. Below are just a few examples of these contradictions.

• Omnipotence — literally the power to do anything (look it up: omni- means "all," and potence is from the Latin for "to be able") — is an abstract concept which cannot logically exist in reality. There's an old puzzler which illustrates this: if an entity is omnipotent, it should be able to create a stone that nobody can lift; but likewise, it should also be able to lift any stone. As this simple example shows, the powers with which an omnipotent entity is endowed directly contradict each other. For those who counter that the Judeo-Christian god is referred to as almighty, rather than omnipotent, we would point out that in fact, neither word is used in the bible, since it wasn't written in English. We would also suggest a thorough perusal of your dictionary.
• Omniscience — the power to know everything (again, you can look it up) — also contradicts itself. An omniscient entity could never be faced with the unexpected, and therefore would not have experiential knowledge of such an incident; not knowing even one thing precludes the possibility of omniscience.
• Omniscience logically conflicts with omnipotence. An omniscient entity would know everything, including what course future events would take. However, knowing the course of the future renders the entity unable to do anything to change that future, as it would then be incorrect as to its predictions and therefore not omniscient — but this inability to change events means that the entity cannot be omnipotent. Additionally, omnipotence would imply a complete lack of knowledge of what it feels like to be unable to do something, and thereby conflicts with omniscience. Both of these examples represent a contradiction between the two powers.
• Both omnipotence and omniscience conflict with the concept of an absolutely benevolent entity — one that is all good and loving — insofar as we can witness in the real world. An absolutely benevolent entity would prevent evil and hardship, unless it was unaware of it (which conflicts with omniscience) or unable to do so (which conflicts with omnipotence).
• The above arguments aside, the most basic problem with the idea of a god (or any supernatural phenomenon) existing is that the argument for it is completely unfounded. Can we prove that your god doesn't exist? No, you can't prove a negative. But all of the "arguments" meant to prove that a god does exist are, quite simply, arguments from ignorance. The theist says, "Can you explain this particular phenomenon?" The rationalist says, "No, not yet." To which the theist replies, "Well, since you don't know the explanation, God did it." That is an absurdity, and a logical pitfall. You can't just make up an explanation for a phenomenon for which you don't yet know the explanation. While science certainly doesn't have all the answers yet, keep in mind that thanks to science, our knowledge expands exponentially with the passage of time. Every time science comes up with an answer, though, the irrationalists push the goalpost back a little further — and when science finally meets that goal, the goalpost is pushed back even further. This constant grasping for gods to explain what we don't know is commonly known as the "God of the Gaps" argument — using religion or some other mumbo-jumbo to fill in the gray areas that science hasn't yet answered. Aside from being illogical, those who make this assertion are buying into a shrinking market as science continues to eliminate these gaps one after another. Deliberate ignorance is a ridiculous way to approach the search for knowledge. If you have faith, more power to you — just don't try to argue that your position is logical or rational.
• Still, all of this logical dithering doesn't address the basic point of God's existential status. The real point is, even if any human concept of a god actually does exist, as far as our empirical senses can perceive, this entity makes no effort to intervene in our affairs or make its existence known, under any circumstances measurable by logic and science. Therefore, whether God exists or not, we have no reason to do anything about it — our lives will go on with or without a deity, and may be much more valuable and full if we don't waste them kowtowing to the alleged authority of an invisible magical superhero in the sky.