Cemeteries in Logan County that are not privately endowed or owned are maintained by the Logan County Cemetery District. The good citizens of Logan County pay taxes to take care of cemeteries that might otherwise be in dispair or lost. For the active cemeteries the cemetery district also keeps track of burials and they have any records that exist for the old cemeteries which are no longer in use. This does not mean the old cemeteries are maintained in pristine shape but it does mean they are at least mowed several times a year.
A list of the cemeteries in Logan County can be found here. Someone has walked the cemeteries in red in the last 10 years and those listings are here. In addition, in the 1960s and early 70s the Decatur Genealogical Society in neighboring Macon County walked many of the cemeteries and has listings available for sale in their publications found on their website which is here.
The Logan County Genealogical & Historical Society sells a CD which contains all the burials in Logan County through a few years ago. You can find more information on their website. That web site is in some transition but the main page should remain the same.