I would argue that the biggest change would be that our society would be more traditional than it is now. Sexual morality and sex roles would be more like they were in the decades before the Pill.
The Pill, first of all, made sex less risky for women. The ability to have sex without having to worry about pregnancy made it possible for women to be more sexually active outside of marriage than they previously were. This has helped to move us away from traditional sexual morality.
Secondly, the Pill made it possible for women to have more certainty about their reproductive lives. It made it much more possible for them to plan pregnancies. This allowed them to be more able to have good careers since they could more or less plan their pregnancies when they wanted them. This made women economically more equal to men which has also helped lead to more social equality.
If the Pill had never been invented, we would probably have a society where sex outside of marriage was rarer and women were not as equal to men as they are today.