The most recent of the Ohio Genealogical Society Quarterly (2013, Vol. 53, Issue 1, pp. 23-38) has the greatest article about the published county histories of the state of Ohio! Professional librarian (retired), Robert Foster Seal has compiled a listing of county histories currently available online digitally "free of charge to all researchers" at FamilySearch, Google Books, Internet Archive, &/or HathiTrust Digital Library. I had not previously heard of HathiTrust, but it was the easiest of the four for me to actually use for my counties!
Most of the books listed are available on more than one of the sites. For instance, the 1881 edition of History of Knox County, Ohio: Its Past and Present is at all four sites, as is the 1880 edition of Morrow County and Ohio. On the other hand, the Historical Atlas of Paulding County, Ohio of 1892 is available only at Internet Archive.
Each of the 88 Ohio counties has at least one book listed, but many have more than one. For example, Ottawa County has only one listed, but Knox County has four and Seneca has five!
It is a great treat to have this resource list readily available in one place. The journal editor added a note saying that OGS will add Seal's list to their website and will accept additions of listings for other histories available at free sites. I am so glad I am an OGS member! I think this article alone was worth the price of my last renewal....! Thank you, OGS, and thank you very much, Mr. Seal!