If you're used to thinking of county lines as fixed, Ohio will throw you a curve.
The county your ancestor lived in is often not the county where their records were filed — because that county may not have existed yet.
When Washington County was created in 1788, it covered most of the Northwest Territory: all of present-day Ohio and beyond. As settlers moved in, the state carved that territory into smaller and smaller pieces. By Ohio statehood in 1803, there were only nine counties. The subdividing kept going for decades, until the 1851 state constitution required any new county to have at least 400 square miles — which effectively ended new county creation. Noble County, formed in 1851, was the last of Ohio's 88 counties.
What this means for your research: a deed, will, or marriage record for an ancestor who lived in, say, 1815 "Licking County" might actually be filed in the courthouse of whatever county Licking was carved from — because the record was created before the split. The land didn't move, but the county it belonged to did.
Before you drive to (or write to) a courthouse, check when your ancestor's county was formed and what its parent county was. Two free tools make this easy:
Ohio County Creation Dates and Parent Counties — a full list of every county, when it formed, and what it was carved from.
Interactive maps showing Ohio county formation from 1788 to 1888, year by year.
A good habit: when you log a record, note the county as it existed on the record date, not just the modern county name. It'll save you a wasted trip and explain why a record you expect to find isn't where you're looking.