Blood tests can be done to help detect metabolic problems like diabetes or thyroid disease that can be affected or revealed during a pregnancy.
At some point in your pregnancy you might have a complete blood count and metabolic panel. If you don't already know your blood type you might have a blood test to see if you are rH negative. If you have had previous transfusions you might have a test to see if you have antibodies to other blood types that could attack you fetus if it has one of those blood types.
If you were a little older you might have a blood test to detect cell free DNA of your baby to see if there are genetic problems.
The answer is that one size does not fit all, every individual may need a different approach and different testing depending on who they are and what conditions they have. You should ask your medical provider to explain what testing is ordered and what its purpose might be.
It possible that your mother and grandmother had no testing at all during their pregnancies. Pregnancy is, after all, a natural condition and could proceed without testing. Modern testing offers a way to diagnose some problems once symptoms occur, or based on a person's medical history. But a normal pregnancy might require no blood tests at all in a young women.
Doug Young, MD