William F. Greenwood (April 19, 1857 – May 2, 1902) was an American Major League Baseball player (mostly a second baseman) for six seasons from 1882 to 1890.

Greenwood was fast and was often among the league leaders in stolen bases, but he usually hit for a mediocre batting average.

[1] For the 1883 season, he signed and was playing for the Merrits of Camden, New Jersey, when Charlie Byrne of a fellow league team, the Brooklyn Grays, bought his contract, along with other Merrits Sam Kimber, Charlie Householder, Frank Fennelly, and Jack Corcoran.

During an 1887 home game, Greenwood was on the receiving end of a collision at second base from St. Louis Browns outfielder Curt Welch.

Compounding his problems was the fact that he liked to drink to excess, so he sometimes got on the bad side of a manager with his behavior.