Gods vary in the scope of their powers. Yahweh, the Christian God, is defined to be the omniscient, omnipotent, and omnibenevolent lone creator of the entire universe. On the other hand, Greek gods such as Hermes and Dionysus are considerably less powerful, occupying a hierarchical pantheon, squabbling with fellow gods, and exhibiting human traits such as anger and jealousy.
By far the most straightforward argument against the existence of a god is that there is no evidence for it. An important principle of science is that extraordinary claims require extraordinary evidence.
In the case of the Christian god, we are asked to explain the existence of a vast, complex, incomprehensible universe by inventing an even more vast, complex, incomprehensible being, which also happens to be intelligent enough to "plan" the entire history of the universe and still micromanage the details enough to answer prayers, account for who will go to heaven and hell, and deal with minutiae like how people deal with seemingly arbitrary rules about sex.
Treated purely as an explanatory device, introducing a god into the universe raises far more questions than it answers. It brings up the obvious question of who created God. Science tends to reason from the complex to the simple, finding explanations of natural phenomena by breaking them down into basic rules. Of all the things we know of in the universe, intelligence in particular is one of the most complex and mysterious phenomena observed. To suppose that we could "explain" the universe by introducing a universe-spanning intelligence is completely backwards from the way science normally operates.
All this would be strictly academic nitpicking if there were any positive evidence for the existence of a god. Yet when pressed for evidence, apologists are notoriously vague. Rather than pointing to specific reasons why anyone should believe in such an improbable being, they point to the Bible as a historically accurate text; they bring up philosophical vagaries such as the first cause argument and the argument from design, and they threaten hell by means of Pascal's wager. No test is ever proposed to demonstrate or falsify the existence of God; God's existence is merely assumed to be a default position (which also invokes argumentum ad populam).
Capitalization of "God"
As a point of grammar, the word "God" is usually capitalized when it refers to a particular god as a proper name; whereas "god" is in lowercase when it refers to one or more of a set of objects. For example: "I do not believe in your god."
Reverential religious texts often take the capitalization a step further when they are talking about their own gods, going so far as to capitalize pronouns that refer to the god. For example: "I love Him"; "We are saved by His grace".