To answer what would happen if there was no God, first I must ask you to define what you mean by "God." Do you mean the Christian God and only the Christian God, or do you mean ALL beings that we would call gods? And also, do you mean if it was never there, or do you mean if it suddenly died?
If you mean all divinity suddenly died, then surely the world would be very different, but we would not know the difference -the divinity influences our actions and from them come our thoughts. We would probably continue life, just with a noticably altered psycology - worship would no longer give that sensation that it gives the faithful, people would not be as driven to do evil, and people would not care to resist temptation when it comes their way.
If you mean all divinity never existed, then we could never exist, because the universe and conciousness itself are part of the divinity network. Something cannot come from nothing if there is no divinity, for if something came from nothing, it would be divinity or have been created by divinity.
Now, if you mean the Christian God suddenly stopped existing...
Chaos. God, in addition to creating the world and holding the universe together, plays a similar role in the divinity network to what a buffer plays in an acid/base solution, except that instead of just "acids" and "bases," you have oodles of categories that all hate eachother and want to compete. God stops the little gods, the ones we are not to worship, from messing with our lives. We are not to worship these gods because worshipping them gives them power, in addition to bringing them into existence. A god is created when humans worship it, and a god dies when humans stop worshipping it and forget about it. Each of these human-made gods has a direct influence on the lives of people (particularly the people that worship them), and God is the only thing stopping them from tearing eachother to shreds and bringing the world down with them. If God suddenly stopped existing, each one of the little gods would start controlling people as much as they can and make war with one another, until all the people eventually killed eachother off, depleting the worship supply of the gods and bringing them down as well.
Think of it this way: Without God, Aphrodite could grab your soul, sweep your willpower under the rug and drive you mad over the image of a beautiful woman. Without God, Hades could reach up from the ground and drag you into the underworld prematurely. Without God, Baal could decide to bring famine to a particular area whenever he felt like it. (Sorry, I don't know much about gods of non-mediterranean areas =/)
God keeps all the human-made "gods" in check, and actively campaigns for people to stop worshipping them and giving them power. Take away God, and it's like you've opened up Pandora's Box.
EDIT: Oh, and the laws of nature (ie, gravity) might disappear too. The lesser gods tend to view nature as an obstacle to get around, while God tries to work within the laws of nature that he set up.
And if God never existed, nothing would exist, as the world came from God, and humans came from the world (God created human from dust), and from humans came the lesser gods. Everything that's not divinity has to have an origin. Anything that would be defined a "God" (with a capital G) would have to exist first for the rest of the existence to exist.
