Games lost by pitchers are often cited and easy to find. Baseball Almanac likes to take things one step further and is pleased to present a handful of consecutive games won records:

Most Consecutive Games Lost Ever
Anthony Young : Twenty-seven from May 6, 1992 to July 24, 1993.
Most Consecutive Games Lost To One Team
Don Sutton : Thirteen from April 23, 1966 to July 24, 1969 vs Chicago.

Most Consecutive Games Lost From Start of Career
Terry Felton : Sixteen from April 18, 1980 to September 12, 1982.

The American League pitchers with the fewest losses who still led their league in games lost are: Ted Gray, Alex Kellner, Bob Lemon, Billy Pierce, Duane Pillette, and Dizzy Trout. All these hurlers had fourteen losses and all led during the 1951 season.

The National League pitchers with the fewest losses who still led their league in games lost are: Don Carman, Orel Hershiser and Ken Hill. All these hurlers had fifteen losses and all led during the 1989 season. Three years later (in 1992) Tom Candiotti & Orel Hershiser (again) tied the record of fifteen originally set in 1989.