In general, God is the single all-powerful entity of the monotheistic Abrahamic religions, the creator of all that is and is solely responsible for all creation - past, present and future.
In Judaism, He is known as YHWH, but usually referred to as HaShem ("the Name") or Adonai ("Master" or "Lord"). Most Christians simply refer to Him as "God" or "Lord," or many variations of this, and some Christian religions refer to Him as Jehovah. In Islam, He is called Allah ("the God"), although He has 99 names, all referring to a specific aspect of the one God. The One God is always to be capitalized when speaking or writing, including He, Him or His.
Generally, God resides in Heaven. He is the creator of Earth and mankind, the first two humans being Adam and Eve. The principal enemy of God is Satan, a rebellious angel cast from Heaven who resides in Hell.
God was lonely.
So God created the angels, so He would have someone to love Him. And they did. But after a while, God was curious about just how much they loved Him. So God announced that He was going to create Humans, a new type of being that could - unlike the angels - choose to worship or ignore God. They would live without the tangible, real presence of God around them.
And all hell broke loose.
Fully half of the angels believed that the world God was intending to create would be unlivable. Humans, without the presence of God, would turn on each other. It would be a world of war, death and blood. These angels rebelled in protest against what they perceived to be a needlessly cruel act of God. And thus, they Fell.
And so God created Humanity, and watched while they tore each other to pieces trying to prove how much they loved Him.
This was okay, but eventually God got lonely again. The angels who remained loved him, yes, and a lot of humans loved him, but was it enough?
He engineered the downfall of a bad man who had gone far in becoming a good one. This man, whose hate was so strong that it froze the fires of Hell itself, became the Saint Of Killers. Unstoppable, to gain his love would be a true challenge. But not quite challenge enough.
So God arranged for a Seraphim, patrolling the edges of Heaven, to meet a demon on the edges of Hell. And He arranged for them to have a child.
And when the child - Genesis - was born, He ran for His life.
He had created a being as powerful as He was, and all that was needed now was to gain its love as well.
Unfortunately for God, Genesis found a home in the body of Jesse Custer, a strong-willed Texas preacher who considered God's abandonment of Heaven to be a betrayal of His responsibilities as a Creator. So Jesse, along with his friends Tulip and Cassidy, went on a quest to find God and make Him answer for His abandonment.
God tried to put Jesse off his quest. He granted Marie L'Angell and her henchmen immunity from Jesse's Genesis-granted powers, and allowed them to murder Tulip. Then He resurrected Tulip and withdrew His protection from Jesse's enemies. For this, has asked Tulip to ask Jesse to give up his quest. Tulip knew it wouldn't work, and said so.
Later, God came to Cassidy, bleeding and broken in the basement of Masada, the French headquarters of The Grail. He chastised Cassidy, and named him Beast due to his vampirism, and told him to give a message to Jesse: Give up the quest and leave God alone. If they meet again, He will kill Jesse.
But Jesse just wouldn't give up. He couldn't understand why God would make such a world as ours and then abandon it. He needed answers. He needed to talk to God.
Jesse got his chance, but he was hardly ready for it. After falling from an airplane at the edge of a nuclear holocaust, God finally came face-to-face with Jesse. He told Jesse that, despite his defiance, He still loved him, and offered His blessing. Jesse wouldn't take it. He accused God of cowardice, and then attempted to use his Voice on Him.
God stopped him and threatened to unmake Jesse unless he begged God's forgiveness. Jesse spat in God's face, for which God sucked out Jesse's left eye. He would have killed Jesse if not for the appearance of the Saint of Killers - the only being in Creation of whom God was afraid. He disappeared and went into hiding again.
Genesis was the problem. It was too powerful, and Jesse was too stubborn. If God appeared again, they would be ready, and God did not want Himself at Jesse's mercy. He just wanted Jesse to love Him.
And that was what they whole thing was about, at least the way Jesse figured it. God had a pathological need to be loved. So He created the angels, and then announced the creation of humans - just to see which of the angels loved Him enough to stay. He created Genesis to see if He could gain the love of an entity just as powerful as Himself. And that was His mistake. As long as Jesse and Genesis were bound together, God was vulnerable.
A chance came from the vampire, Cassidy. He offered God a deal. Cassidy would get into a fight with Custer - not very difficult - and beat him near to death. Then God could step in, remove Genesis, and be home free. The only condition was that both Jesse and Cassidy live through the event, no matter what.
Little did God know that Jesse had already formed his own plan, ignorant of Cassidy's. Jesse's plan was to die.
His death would release Genesis, at which point God would make a run for His throne in Heaven. The Saint of Killers would be waiting, with his guns drawn and his mind turned to revenge.
When Jesse died, God went back to Heaven having fulfilled his promise to the vampire - Custer and Cassidy were once again alive and whole. He came through the gates of Heaven to find the entire Host of angels dead, and the Saint of Killers in the middle of the carnage.
God tried to bargain with the Saint, offering to return his life, his humanity, his family to him. He begged the Saint to tell him what he wanted. The Saint replied, "To rest." And shot God dead.
Avengelyne is a fallen angel, cast from Heaven by God for questioning him. God's angels are known as the Warhost, which is a mix of biblical angels as well as some original to the series.
The Big Two - Marvel & DC
The Abrahamic God is generally avoided in the big two comic publishers for fear of offending religious people. In Marvel Yahweh is mentioned as a member of the Council of Godheads.
God is omnipotent, omnipresent and omniscient.