Consecutive championship teams.

1951 New York Yankees celebrate 1950.
via Wiki Commons

No surprise: the New York Yankees have the most and the longest streaks.

5: 1949-1953
4. 1936-1939
3. 1998-2000 (tied with Oakland)
2. 1927-1928
2. 1961-1962
2. 1977-1978

Can the Red Sox repeat? They haven't since Babe Ruth left.  Thursday, March 6, 2014

The most recent team to repeat: the New York Yankees 1998, 1999, 2000...

The Yankees are the only team to win consecutive championships since the formation of three divisions in each conference in 1994 (no tournament that season).  Three divisions and four teams qualifying for the tournament essentially made the odds of winning a championship about twice as hard as that under the system from 1903 through 1960 when one of eight finished first and then played in the WS.  In 1961 modern expansion started and in 1969 each of the two major leagues were split into two six team divisions with a five or, starting in 1985, seven game series determining which team reached the championship series.
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Winning consecutive championship is much more rare than one might think.  Since 1905 the National League/Conference winner most often has been the Dodgers and the Cardinals but neither team has won consecutive championships.  Teams in existence in 1905 that never won consecutive championships:

Dodgers played in consecutive championship series:
1952 lost to Yankees
1953 lost to Yankees

1955 beat Yankees
1956 lost to Yankees

1965 beat Twins
1966 lost to Orioles

1977 lost to Yankees
1978 lost to Yankees  Last time two teams played each other in consecutive years.

Cardinals played in consecutive championship series:
1930 lost to Athletics
1931 beat Athletics

1942 beat Yankees
1943 lost to Yankees
1944 beat Browns

1967 beat Red Sox
1968 lost to Tigers

Detroit Tigers: Only team to lose three consecutive championship series: 1907-1909; also split in 1934 (lost), 1935 (won)

St. Louis Browns/Baltimore Orioles: played in three consecutive championship series: 1969 (lost), 1970 (won), 1971 (lost)

Washington Senators/Texas Rangers played in consecutive championship series:
1924 beat Giants
1925 lost to Pirates

2010 lost to Giants
2011 lost to Cardinals

played in consecutive championship series once:
Boston/Milwaukee/Atlanta Braves  1957 (won), 1958 (lost)
Philadelphia Phillies: 2008 (won), 2009 (lost)

Never played in consecutive championship series:
Chicago White Sox
Pittsburgh Pirates
Cleveland Indians

The Chicago Cubs are the first repeat winner but the Cubs have not won an individual championship since then: 1907-1908.

The Athletics are the only team other than the Yankees with multiple streaks:
3. 1972-1974
2. 1929-1930
2. 1910-1911.

Yankees and Giants only teams to play each other in three consecutive championship series:
1921 Giants won
1922 Giants won
1923 Yankees won

Most winning streaks occurred before expansion in 1961.  There was one from 1961-1968 : Yankees 1961-1962, the only team in those eight years to reach the final series in consecutive years.  The American League (AL) expanded from 8 to 10 teams in 1961, the National League (NL) in 1962.  There were two divisions 1969-1993 (one extra series), then three divisions. (two extra series).  Teams reached the final series less frequently with more preliminary rounds.

Since 1995 teams that reached the final series in consecutive years:
1998-2001 Yankees, winning the first three and losing the fourth in the bottom of the 9th inning in game seven
2010-2011 Texas Rangers: lost both
2008-2009 Philadelphia Phillies: won, lost

Since 1995 the only teams to face each other multiple times:
Yankees - Atlanta Braves: 1996, 1998; Yanks won both
Red Sox - Cardinals: 2004, 2013; Red Sox won both

Since 1995 multiple championships:
5 Yankees 1996, 1998, 1999, 2000, 2009
3 Red Sox 2004, 2007, 2013
2 Marlins 1997, 2003
2 Giants 2010, 2012
2 Cardinals 2006, 2011

Only five teams have won in the last eight years: six in the last ten.

Streaks from 1969-1993:
1992-1993 Toronto Blue Jays
1977-1978 New York Yankees
1975-1976 Cincinnati Reds
1972, 1973, 1974 Oakland Athletics

Year	Winning Team	Losing Team	W	L	Manager	Player	Pitcher
2000	New York Yankees	New York Mets	4	1	Joe Torre	Jorge Posada	Roger Clemens
1999	New York Yankees	Atlana Braves	4	0	Joe Torre	Derek Jeter	David Cone
1998	New York Yankees	San Diego Padres	4	0	Joe Torre	Bernie Williams	David Cone
1993	Toronto Blue Jays	Philadelphia Phillies	4	2	Cito Gaston	John Olerud	Juan Guzman
1992	Toronto Blue Jays	Atlana Braves	4	2	Cito Gaston	Roberto Alomar	Juan Guzman
1978	New York Yankees	Los Angeles Dodgers	4	2	Bob Lemon	Graig Nettles	Ron Guidry
1977	New York Yankees	Los Angeles Dodgers	4	2	Billy Martin	Graig Nettles	Ron Guidry
1976	Cincinnati Reds	New York Yankees	4	0	Sparky Anderson	Joe Morgan	Pat Zachry
1975	Cincinnati Reds	Boston Red Sox	4	3	Sparky Anderson	Joe Morgan	Don Gullett
1974	Oakland Athletics	Los Angeles Dodgers	4	1	Alvin Dark	Reggie Jackson	Catfish Hunter
1973	Oakland Athletics	New York Mets	4	3	Dick Williams	Reggie Jackson	Ken Holtzman
1972	Oakland Athletics	Cincinnati Reds	4	3	Dick Williams	Reggie Jackson	Catfish Hunter
1962	New York Yankees	San Francisco Giants	4	3	Ralph Houk	Mickey Mantle	Whitey Ford
1961	New York Yankees	Cincinnati Reds	4	1	Ralph Houk	Mickey Mantle	Whitey Ford
1953	New York Yankees	Brooklyn Dodgers	4		Casey Stengel	Yogi Berra	Whitey Ford
1952	New York Yankees	Brooklyn Dodgers	4	3	Casey Stengel	Mickey Mantle	Allie Reynolds
1951	New York Yankees	New York Giants	4	2	Casey Stengel	Yogi Berra	Allie Reynolds
1950	New York Yankees	Philadelphia Phillies	4	0	Casey Stengel	Phil Rizzuto	Eddie Lopat
1949	New York Yankees	Brooklyn Dodgers	4	1	Casey Stengel	Tommy Henrich	Vic Raschi
1939	New York Yankees	Cincinnati Reds	4	0	Joe McCarthy	Joe DiMaggio	Red Ruffing
1938	New York Yankees	Chicago Cubs	4	0	Joe McCarthy	Joe DiMaggio	Ruffing/Gomez
1937	New York Yankees	New York Giants	4	1	Joe McCarthy	Joe DiMaggio	Lefty Gomez
1936	New York Yankees	New York Giants	4	2	Joe McCarthy	Lou Gehrig	Red Ruffing
1930	Philadelphia Athletics	St. Louis Cardinals	4	2	Connie Mack	Al Simmons	Lefty Grove
1929	Philadelphia Athletics	Chicago Cubs	4	1	Connie Mack	Jimmie Foxx	Lefty Grove
1928	New York Yankees	St. Louis Cardinals	4	0	Miller Huggins	Babe Ruth	George Pipgras
1927	New York Yankees	Pittsburgh Pirates	4	0	Miller Huggins	Babe Ruth	Waite Hoyt
1922	New York Giants	New York Yankees	4	0	John McGraw	Irish Meusel	Rosy Ryan
1921	New York Giants	New York Yankees	5	3	John McGraw	Frankie Frisch	Jesse Barnes
1916	Boston Red Sox	Brooklyn Robins	4	1	Bill Carrigan	Larry Gardner	Babe Ruth
1915	Boston Red Sox	Philadelphia Phillies	4	1	Bill Carrigan	Tris Speaker	Ernie Shore
1911	Philadelphia Athletics	New York Giants	4	2	Connie Mack	Eddie Collins	Eddie Plank
1910	Philadelphia Athletics	Chicago Cubs	4	1	Connie Mack	Eddie Collins	Jack Coombs
1908	Chicago Cubs	Detroit Tigers	4	1	Frank Chance	Johnny Evers	Mordecai Brown
1907	Chicago Cubs	Detroit Tigers	4	0	Frank Chance	Frank Chance	Orval Overall