33, Los Angeles Lakers started its winning streak on November 05, 1971 when they beat the Baltimore Bullets, 110-106 and went to win until January 07, 1972 when they beat the Atlanta Hawks, 134-90 and two days later, Kareem Abdul-Jabbar and the Milwaukee Bucks finally ended the winning spree by scoring a 120-104 win and snapping Lakers' 33-game winning streak.
The San Antonio Spurs won 12 playoff games in a row in 1999.
In other news:
The best record for an NBA champion belongs to the 2001 LA Lakers, where they went 15-1 (they are also the only team in NBA history to reach the NBA finals undefeated, they lost the first game to the 76ers in the finals but they won 4 games in a row after the lone loss). Looks like I forgot that the '88-'89 Lakers also made it to the finals undefeated, only to lose to Detroit in a sweep. (Magic Johnson and Byron Scott got injured in the conference finals.)
And in case you were wondering the best regular season record is the 1996-97 Chicago Bulls where they went 72-10 and the longest winning streak for an NBA franchise is 33 games in a row (Which includes the longest road winning streak) for the 1971-72 LA Lakers, they also finished the season with a 69-13 record (which stood until the 1996-97 Bulls with a 72-10 record) and won the championship.
15-0 by the Washington Capitols in 1948-49 season (November 3-December 4, 1948)
15-0 by the Houston Rockets in 1993-94 season (November 5-December 2, 1993) a tie
33 LA Lakers (11/5/71 - 1/7/72) 20 Milwaukee (2/6/71 - 3/8/71) 19 LA Lakers (2/4/00 - 3/13/00) Soon to be 47 by the 08-09 Boston Celtics
11 games
The 07-08 Houston Rockets with 22 consecutive wins.
In the 2008-2009 season, Boston went on a 19-game winning streak, which is a franchise record, and fifth in NBA's all time winning streak records.
44-Chicago, March 30, 1995-April 4, 1996 (7 games in 1994-95; 37 games in 1995-96)
The Boston Celtics' streak of 8 consecutive NBA championships is the longest streak of consecutive championships in U.S. professional sports history
UCLA's 88 game win streak is the longest in mens basketball
Currently, the Milwaukee Bucks hold the third longest winning streak at 20 games, which they set in the 1970-1971 season.
SA Spurs 11 two times
11 games
Los Angeles Lakers with 33 straight wins
The Bucks 20 game winning streak began February 6 and ended March 8 in 1971.
The 07-08 Houston Rockets with 22 consecutive wins.
1971-72 Los Angeles Lakers The team went 33 matches unbeaten
6
In the 2008-2009 season, Boston went on a 19-game winning streak, which is a franchise record, and fifth in NBA's all time winning streak records.
Clippers
New Jersey Nets with an 0-18 losing streak