On the FamilySearch.org website if you arrow down to United States, then go to Ohio there are 2 different collections of marriage records for Ohio. Some of the records give names of parents as well as names of the people marrying. Some are less complete. I think the last time I checked the "Ohio County Marriages" database was only 75% complete, but it is a wonderful resource listing over 3 million records.

Good luck in your search.

Nancy Smith