What would the world be like if marriage did not exist?

I think it would kinda suck ... Cos big promises are AWESOME !  Or being faced with them and saying NO !  Just being confronted with that kinda dicision is good :) I'm never gonna get married again cos I said so .. But that's someting I know about me ... So that's good :)

Everything except the earth has a shelf life.

We have a perfect example now, in one aspect. We see that the children today suffer because of not growing up in a two parent household where they can see their parents working together to nurture them, give them a sound moral foundation and help them to become productive adults. Also it has been my belief that we as humans need commitment and marriage is the ultimate commitment. The bible tells us that a man will leave his father and mother and stick to his wife and the two will become one flesh. When this counsel is ignored, there is a breakdown in communication, which leads to mistrust

From a moral stand point? In most developd countries divorce is fairly easy so I am not sure much would change. In less developed countries or countries where religion governs things would be drastically different. From a legal stand point it where things can get tricky, especially if children are involved. 

I would assume some sort of cohabitation would come into effect like people do when they're not married: As in lovers living with each other.

Marriage is simply a legal proceeding and a ritual. It's not needed to exclaim someone's love for another, but it's simply something that anyone can do to further that claim to others.

then children wouldn't be born.

Well, the formal wear industry would surely go bankrupt; people could spend more time at work or play, and less money on jewelry, flowers, sedatives and divorce lawyers.