I liked some responses ... but I think it will be less dramatic than that ...
In all honesty ... the OP question is a hypothetical question ... the question is a trick question because according to my understanding "What if we all stopped getting married" is far more deeper rooted that simply a matter of cultural practices ... Marriage is present within many of the uncivilised peoples.
If we all stopped getting married then it would mean that we would all NEED to stop a part of our innate natural condition ... that can only be manifest if we stop loving, and stop feeling commitment, stop feeling jealousy, stop feeling possessive - when these things stop then we will stop marriage ... in order for ALL people to stop marriage then ALL people would have to stop these traits first ...
Because if these things were still there then it is inevitable that SOME people will choose to marry even if marriage becomes outlawed ... people will secretly choose to devote themselves to another person through some symbolic act and declaration ... to mark their focus to that person and promise they are not going to focus on another person.
At the fundamental level marriage is an economic arrangement for women (traditionally). For modern women who can financially support themselves, marriage is a 'vehicle' to have children.
In the marriage-less hypothetical society some people would still pair up and have children but overall there will be far fewer children born. At some point governments will step in and give incentives to single women to have babies. Single motherhood will be subsidized. Free sperm banks and fertilization procedures, maternity care, long paid maternity leaves, day care facilities for children up to school going age so mothers can keep working, free healthcare and education ofcourse, and perhaps stipends for children below 18. Basically the common woman wouldn't need a man to bear and raise a child. This is also a society that feminism in west is striving for.
In such a society womens outlook towards relationships with men would be very different and they will choose men only out of desire. Currently women's preferences in men are shaped by many pressures even when they marry and have relationships with men because of 'love'
Men would definitely be the losers in that society. It makes sense that it were men who devised the institution of marriage to protect their own interests.
I am not surprised that all who have posted in this thread including chacha Ghalib, TLK and psyah all respected members have not heard about two communities one in China and the other in the South Pacific where marriage does not exist.
**You ask why it is so, because in both places it is the Women who rule the communities, for example in China young men looking for wives are welcome but after they get comfortable ** **with the girls and make them pregnant they are told to depart, go back where they came from because that disrupts the social order, the girls and the Mothers do not want Fathers sticking around telling the Women how things will be run.
The second community was discovered by a beach bum who went to the South Pacific and lived on the beach, there women or young girls approach men have a relationship until they are pregnant then it syonara buddy the pregnant girl goes back to her Mom and raise her child, with no paternal rights or obligations for the sperm doner**
**So boys and girls this concept of No Marriage is not new, as we all know **it is very successful in the animal kingdom…ever heard of "Queen Bee" **and all her army of drones **
indirectly. if traffic is reduced it would resolve server busy issue, simple 
**with the girls and make them pregnant they are told to depart, go back where they came from because that disrupts the social order, the girls and the Mothers do not want Fathers sticking around telling the Women how things will be run.
