The late Dorothy Riker, an editor of The Hoosier Genealogist, started the project years ago. Volunteers have expanded the index to include marriage information through 1850 from courthouses in all counties that kept records, plus marriages mentioned in Quaker monthly meeting notes and St. Francis Xavier Church (in Vicennes) records. That adds up to around 330,000 marriages recorded in the database.
You can search on the bride or groom. Results link to the persons full name, name of his or her spouse, the date of the marriage and the county where it took place.
Then you can look for the original record on Family History Library microfilm, or request it from the county court clerk (for contact information, go to the state courts Web site and use the Information by County dropdown menu on the left).