The yearly leader in both the American & National League since 1901, for complete games, are all here on Baseball Almanac; as well as the top one-hundred all-time leaders and top one-hundred single season leaders.
Jack Taylor of the St. Louis Cardinals had a National League record (and overall Major League record) thirty-nine consecutive complete games in 1904 while Bill Dinneen of the Boston Americans had an American League record thirty-seven consecutive complete games — also in 1904.
Did you know that the longest / most innings pitched during one complete game by one pitcher is twenty-six? That record is held by two pitchers — Leon Cadore of Brooklyn & Joe Oeschger of Boston — who faced off against each other on May 1, 1920 both setting the record during a marathon 1-1 tie contest.