Cemetery Record research is a very important element in genealogical research. Some of my personnel best cemetery hunts have happened in Putnam Co., OH. My family descends from the Continental area. I have spent some time searching through the Crow, Myers and Varner cemeteries in that area.
Cemeteries come in three forms. They are the church burial yard, public cemeteries and family burial plots. If you are fortunate to have a person buried in a church cemetery the church will often have the records for the burial. This information is similar to a death certificate, but will often include more information. Public cemeteries also have burial records and these are often stored at the local sexton's office or with the township. Family burial plots are often not as well covered, but some records are kept with the township.
A note on rubbings of the stones. This practice is frowned on by most people in the genealogy field. The exposure to weather has resulted in many stones be difficult to read. Rubbings only help in more destruction to the surface of the stone. Use common sense when you are in the cemetery.
Here is a good link for locating cemeteries in Putnam Co. OH.