Here are a couple of websites I found:

http://backpackohio.com/index.html
http://www.dnr.state.oh.us/parks/outdoorfun/backpacking/tabid/492/Default.aspx

There's a good bit of overlap, but there's more places to go than I realized.

You might also be interested in two books by Robert Ruchhoft: Backpack Loops and Long Day Trail Hikes in Southern Ohio, and Kentucky's Land of the Arches: The Red River Gorge in the Daniel Boone National Forest and Natural Bridge State Park. (OK, that last one isn't in Ohio - but it's close by.)