An international cycling map created from OSM data is available, provided by Andy Allan. The map rendering is still being improved, the data are updated every few days. It shows National Cycle Network cycle routes, other regional and local routes, and other cycling-specific features, such as:
dedicated cycle tracks and lanes
contours and hill colouring
bicycle parking
bike shops, toilets, drinking fountains, even pubs!
proposed bike routes (or numbering protocols), contrasted with the Lonvia map, below, which does not show proposed routes, but actual routes only
CyclOSM A free cycle-oriented map with more features than OpenCycleMap. See its wiki page CyclOSM.
Waymarked Trails: Cycling by Sarah Hoffman is a layer superimposed over mapnik (Standard Map Layer) which shows marked cycle routes around the world. Updated minutely, it renders actual routes without the state=proposed tag. Therefore no proposed routes (or proposed numbering protocols) are displayed.
Believed to partially follow the Great Ohio Lake-to-River Greenway in eastern Ohio but otherwise follows State Bike Route K, which has not been mapped. Is there a published Route K map available? (in which case K should be entered into OSM as an rcn)
Mark all member relations as network=rcn + cycle_network=US:OH + ref=number. The lettered routes below are designated by ODOT; tag them as operator=Ohio Department of Transportation. (Most other routes are maintained by county park districts. For such routes that cross county lines, place the operator=* tag on the individual ways, not the relation.)
From southern terminus at the Kentucky state line north to Newtown.
E
F
J
K
N
CT
Cardinal Trail
County bike routes
In counties that maintain a distinct county route system, mark relations as network=lcn + cycle_network=US:OH:XYZ + ref=number (optional), where XYZ is the three-letter county code found at Ohio#County abbreviations. Here are some known county bicycle route networks: