Kansas City Royals
1st longest; 'bout 26 2nd longest; 'bout 24
94 games by the Tignish Aces.
The Detroit red wings with 19 going for 20 this year
The Pittsburgh Pirates (1993-2010) hold the current record for professional sports-18 straight losing seasons.
Wartburg Wrestling in Division III has won 20 consecutive IIAC Titles and has not lost a IIAC dual meet since 1993.
Arnold Palmer, professional golfer. The previous answer was extremely misleading as hundreds of players have gone well past 20 years.
Don Criqui has the longest tenure in sports radio.
The NCAA basketball tournament
The Detroit Red Wings just made their 19th straight appearance in the NHL playoffs, if you're wondering who hold the longest strreak