The National Center for Health Statistics tracks the number and percentage of births to unmarried women because it is a key social indicator. According to the Federal Interagency Forum on Child and Family Statistics:
Children of unmarried mothers are at higher risk of having adverse birth outcomes, such as low birthweight and infant mortality, and are more likely to live in poverty than children of married mothers.
In 2004, 35.8% of all live births were to unmarried women. Compare and contrast that to 14.3% in 1970.
Numbers of births to unmarried women and their percentage of the universe of live births from 1970 through 2004 is available here.
Two good reports we have produced on the subject are Births to Unmarried Mothers: United States, 1980-92 and Nonmarital Childbearing in the United States, 1940-99.