I can go to the local court house and make copies of my ancestors’ marriage licenses dating back to the 1840s, long before Jim Crow laws.
here is what wiki says on the issue:
For most of Western history, marriage was a private contract between two families. Until the 16th-century, Christian churches accepted the validity of a marriage on the basis of a couple’s declarations. If two people claimed that they had exchanged marital vows—even without witnesses—the Catholic Church accepted that they were validly married.
Some states in the US hold that public cohabitation can be sufficient evidence of a valid marriage. Marriage license application records from government authorities are widely available starting from the mid-19th century. Some are available dating from the 17th century in colonial America.[1] Marriage licenses have been required since 1639 in Massachusetts, with their use gradually expanding to other jurisdictions.[2] These prohibitions have changed throughout history. In the 1920s, they were used by 38 states to prohibit whites from marrying blacks, mulattos, Japanese, Chinese, Indians, Mongolians, Malays or Filipinos without a state approved license. At least 32 nations have established significant prohibitions on same-sex marriage.[3]
http://en.wikipedia.org/wiki/Marriage_license
So, as stated above, the licensing of marriage by the state is fairly recent concept. Throughout most of the history of western civilization, it was not licensed.