While the simple answer might be 1973 with the Roe v. Wade decision, the history of abortion’s decriminalization occurred on a state-by-state basis—much like its criminalization.
In colonial America, abortion was dealt with in a manner according to English common law. Abortion was typically only frowned upon, or penalized, when it occurred after “quickening,”—when a woman felt fetal movement—because it suggested that the fetus had manifested into its own separate being. Quickening could vary from women to woman, and sometimes as late as four months. Additionally, it was only penalized because it was typically seen as some kind cover-up for improper sexual relations.
States began to draft abortion legislation in the first half of the 19th century and by 1880, every state had an abortion statute. Most of these early abortion statutes were designed to protect women from medical quacks far from the established centers of American medicine—Philadelphia, New York, and Boston, for example. These early statutes (for the most part) punished only the provider of the abortion, not the woman, and either did not apply to physicians, or did not apply if the abortion was necessary to preserve the life of the woman. Therefore, except under these special circumstances, abortion was illegal.