The 2002 Oakland Athletics had the logest win streak in baseball history with 20 wins.
I've read that Ted Williams had an 84-game streak in 1949, and DiMaggio's 56-game hitting streak was part of a 74-game on-base streak. But, since 1961 when the necessary stats started being recorded, the longest streak is Orlando Cabrera's 63 in 2006.
The most consecutive World Series lost is 7 by the Chicago Cubs (1945, 1938, 1935, 1932, 1929, 1918, 1910). The most consecutive games lost in the World Series is 8 by the Philadelphia Phillies (last 4 games in 1915 and all four games in 1950). The New York Yankees went winless in 9 consecutive games (last 3 games in 1921, all five games in 1922, and the first game in 1923) but one of the games in the 1922 World Series ended in a tie.
As far as MLB is concerned, the longest losing streak in 23 games held by the 1889 Pittsburgh Alleghenys (soon to be Pirates) and the 1961 Philadelphia Phillies.
The longest losing streak is 23 games in a row by 95-96 Grizzlies and 97-98 Nuggets.
That would be his current losing streak of 104 races.
Michael Waltrip had the longest losing streak before winning at the Daytona 500 in 2001.
Pittsburgh pirates at 18 straight and counting
New Jersey Nets with an 0-18 losing streak
The Chicago Cubs 2008 longest losing streak was 6 games between August 30 and September 6.