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.
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".
The single most used argument against the existence of God, by far, is that there is no evidence for his existence. An important principle of science is that extraordinary claims require extraordinary evidence.