(Rich) women would travel overseas to have abortions.
There would be more unwanted children and possibly more babies available for childless couples to adopt, but also more neglected children.
More women - probably younger ones in particular - would kill themselves, either directly committing suicide or by trying to cause an abortion (hot baths, falling down stairs) and would die that way.
Depending on how total the ban was, women would die from not being allowed life-saving drugs or treatment during pregnancy.
Now we have DNA testing, more men - possibly young men in particular - would be forced to take on financial responsibility for accidental children.
There would be more “backstreet abortions” and more doctors would carry out illegal abortions.
There would be greater infanticide, and more neo-natals abandoned in doorways, etc.
There would be more children born with congenital defects, Downs Syndrome. NB: this is not a pro-eugenics statement - just an observation that many pregnancies are currently terminated after amniocentesis testing(sp?) and would not be if abortion was banned.
Most of the above still happen despite abortion being legal, but they would undoubtedly increase if it was banned.
Personally speaking, if I had an unwanted pregancy and they changed the law, I would go overseas if I could afford it, if not, I would find a sympathetic doctor, if not, I would go backstreet (obviously not a rusty-coathanger, but maybe an ex-midwife, whatever backstreet abortioners used to be. I am sure it rarely literally means “up a dark alley”).
There would be more use of contraceptives.