State Route 637 (SR 637) is a 26.13-mile (42.05 km) state route that runs between U.S. Route 224 (US 224) and Arthur in the US state of Ohio. Most of the route is a rural two-lane highway and passes through farmland. The highway was first signed in 1937 on much the same alignment as today, only reaching as far north as an intersection with SR 111. Some of the highway was paved in 1939, with the rest of the route being paved in 1948. SR 637 was extended in 1983, to an intersection with SR 66.