I think this is close to a full list of the teams that participated.
Franchise known as TEXAS RANGERS (0):
None.
A. Franchise formerly known as the Tampa Bay Devil Rays (1):
1. 2008 Tampa Bay Rays (97-65, Lost in the World Series, 4-1, to the Phillies). (AL Champs)
B. Franchise known as the SEATTLE MARINERS (1):
1. 2001 Seattle Mariners (116-46, Lost American League Championship, 4-1 to NY Yanks.)
C. Franchise known as the Giants (8):
1. 1951 New York Giants (98-59, Lost the World Series, 4-2, to the Yankees). (NL Champs)
2. 1952 New York Giants (92-62, finished 2nd, NL, 4.5 GB Brooklyn)
3. 1954 New York Giants (97-57, won WS, 4-0 (Cleveland))
4. 1962 San Francisco Giants (103-62, lost WORLD SERIES, 4-3 to New York Yankees). (NL Champs)
5. 1993 San Francisco Giants (103-59, 2nd place, 1 GB Atlanta Braves, NL West)
6. 2000 San Francisco Giants (97-65, Lost LDS to New York Mets, 3-1.)
7. 2002 San Francisco Giants (95-66, Lost World Series to Angels, 4-3.) (NL Champs)
8. 2003 San Francisco Giants (100-61, Lost the LDS to the Florida Marlins, 3-1)
D Franchise known famously as the San Diego Padres (1):
(Their years
1. 1998 San Diego Padres (98-64, Lost WORLD SERIES to New York Yankees, 4-0.) (N.L. Champs)
E. Franchise famously known as the Pittsburgh Pirates (6):
1. 1960 Pittsburgh Pirates (95-59, WORLD SERIES WINNERS, 4-3 over Yankees.)
2. 1971 Pittsburgh Pirates (97-65, WORLD SERIES WINNERS, 4-3 over Orioles.)
3. 1972 Pittsburgh Pirates (96-59, Lost the National League Championship to the Reds, 3-2)
4. 1979 Pittsburgh Pirates (98-64, WORLD SERIES WINNERS, 4-3 over Baltimore.)
5. 1991 Pittsburgh Pirates (98-64, Lost NLCS, 4-3, to the Braves)
6. 2015 Pittsburgh Pirates (98-64, lost NL Wild Card playoff to Chicago Cubs, 1-0)
f. Philadelphia Phillies (5):
1. 1976 Philadelphia Phillies (101-61, Lost NL Championship, 3-0, vs. Reds)
2. 1977 Philadelphia Phillies (101-61, Lost NL Championship, 3-1, vs. LA Dodgers)
3. 1993 Philadelphia Phillies (97-65, Lost World Series, 4-2 to Blue Jays) (N.L. Champs)
4. 2010 Philadelphia Phillies (97-65, Lost NLCS, 4-2 to Giants)
5. 2011 Philadelphia Phillies (102-60, Lost LDS to Cardinals, 3-2)
G. Franchise known as the A’s (8):
1. 1971 Oakland Athletics (101-60, lost the American League Championship to Baltimore Orioles, 3-0.)
2. 1972 Oakland Athletics (93-62, WORLD SERIES WINNERS, 4-3, over Reds.)
3. 1975 Oakland Athletics (98-64, lost ALCS to Red Sox, 3-0.)
4. 1988 Oakland Athletics (104-58, lost WS 4-1 to LA Dodgers)
5. 1989 Oakland Athletics (99-63, won world series 4-0 over SF Giants)
6. 1990 Oakland Athletics. (103-59, lost World Series, 4-0, vs. Reds.)
7. 2001 Oakland Athletics (102-60, lost LDS to Yanks, 3-2)
8. 2002 Oakland Athletics (103-59, lost LDS to Twins, 3-2)
H. Franchise currently known as the Minnesota Twins (3):
1. 1965 Minnesota Twins (102-60, Lost World Series, 4-3 to LA Dodgers)
2. 1969 Minnesota Twins (97-65, Lost American League Championship to Orioles, 3-0.)
3. 1970 Minnesota Twins (98-64, Lost American League Championship to Orioles, 3-0.)
Milwaukee Brewers (0):
None.
Franchise known as the Marlins (0):
None.
I. Franchise known most popularly as the Dodgers (15):
1942 Brooklyn Dodgers (104-50, 2 GB the Cardinals)
1946 Brooklyn Dodgers (96-60, 2 GB the Cardinals)
1947 Brooklyn Dodgers (94-60, Lost World Series to New York Yankees, 3-4.)
1949 Brooklyn Dodgers (97-57, Lost in World Series to Yankees, 4-1.)
5. 1951 Brooklyn Dodgers (97-60, 2nd place, NL, (NEW YORK GIANTS))
1952 Brooklyn Dodgers (96-57, Lost WORLD SERIES to New York Yankees, 3-4.) (N.L. Champs)
1953 Brooklyn Dodgers (105-49, lost WORLD SERIES, 4-2 to NY Yanks). N.L Champs.
1954 Brooklyn Dodgers (92-62, finished 2nd, NL, (5 GB of New York Giants))
1955 Brooklyn Dodgers (98-55, WORLD SERIES WINNERS, 4-3, vs. N.Y. Yanks!)
10. 1956 Brooklyn Dodgers (93-61, lost the series, to the Yankees, 4-3). (N.L. CHAMPIONS)
1962 Los Angeles Dodgers (102-63, finished 2nd to San Francisco Giants)
1963 Los Angeles Dodgers (99-63, WON WORLD SERIES, 4-0 Over Yanks)
1965 Los Angeles Dodgers (97-65, WON WORLD SERIES, 4-3 vs. Minnesota Twins)
1974 LA Dodgers (102-60, lost WS 4-1 to the Oakland Athletics)
15. 1977 Los Angeles Dodgers (98-64, Lost in World Series, 4-2 to New York Yankees)
(2017)
J. Franchise known as the ANGELS (4):
2002 Anaheim Angels, (99-63, won World Series, 4-3 over the SF Giants)
2008 Los Angeles Angels of Anaheim (100-62, lost a LDS to the Boston Red Sox, 3-1.)
2009 Los Angeles Angels of Anaheim (97-65, lost the American League Championship to the New York Yankees.)
2014 Los Angeles Angels of Anaheim (98-64, lost an LDS to the KC Royals, 3-0)
K. Franchise currently known as the KANSAS CITY ROYALS (2):
1977 Kansas City Royals (102-60, Lost American League Championship to New York Yankees, 3-2.)
1980 Kansas City Royals (97-65, Lost the World Series to the Phils, 2-4.)
L. Franchise Currently known as the HOUSTON ASTROS (2):
1. 1998 Houston Astros (102-60, lost in the LDS to the Padres.)
2. 1999 Houston Astros (97-65, lost in the LDS to the Braves.)
(2017)
M. Franchise currently known as DETROIT TIGERS (6):
1. 1946 Detroit Tigers (92-62, finished 2nd in AL, 12 GB Red Sox.)
2. 1950 Detroit Tigers (95-59, finished 2nd in AL, 3 GB Yankees.)
3. 1961 Detroit Tigers (101-61, finished 2nd in AL, 8 GB Damn Yanx.)
4. 1968 Detroit Tigers (103-59, WON WORLD SERIES 4-3, over St. Louis Cardinals)
5. 1984 Detroit Tigers (104-58, WON WORLD SERIES, 4-1 over Padres.)
6. 1987 Detroit Tigers (98-64, Lost American League Championship to Twins, 4-1)
Franchise currently known as COLORADO ROCKIES (0):
None.
N. Franchise currently known as New York Yankees (32):
25. 1942 New York Yankees (103-51, lost World Series to the St. Louis Cardinals, 1-4.) (A.L. Champs)
1. 1943 New York Yankees (98-56, won World Series over St. Louis Cardinals, 4-1.)
2. 1947 New York Yankees (97-57, won World Series 4-3 over the Brooklyn Dodgers)
3. 1948 New York Yankees (94-60, finished 3rd 2.5 GB Cleveland Indians)
4. 1949 New York Yankees (97-57, WON WORLD SERIES, 4-1 over Brooklyn Dodgers)
5. 1950 New York Yankees (98-56, WON WORLD SERIES over Phillies, 4-0.)
6. 1951 New York Yankees (98-56, WON WORLD SERIES over NYG, 4-2.)
1952 New York Yankees (95-59, WON WORLD SERIES over Brooklyn, 4-3.)
7. 1953. New York Yankees (99-52, WON WORLD SERIES 4-2 over Brooklyn.)
1954 New York Yankees (103-51, finished 2nd, 8 games behind them Indians.)
1955 New York Yankees (96-58, lost World Series 3-4 to Brooklyn Dodgers.)
8. 1956 New York Yankees (97-57, won World Series, 4-3 over Brooklyn Dodgers.)
9. 1957. New York Yankees (98-56, lost World Series to Milwaukee Braves, 4-3.) (A.L. Champs)
1958. New York Yankees (92-62, won World Series vs. Milwaukee Braves, 4-3.)
10. 1960 NY Yankees (97-57, Lost the World Series 4-3 to Pittsburgh.)
11. 1961 New York Yankees (109-53, WORLD SERIES WINNERS, 4-1, Reds.)
12. 1963 New York Yankees (104-57, Lost World Series 4-0 to L.A. Dodgers.)
13. 1964 New York Yankees (99-63, Lost the World Series, 4-3, to the Cardinals.)
1976 New York Yankees (97-62, Lost World Series, Cincinnati Reds, 4-0) (A.L. Champs)
14. 1977 New York Yankees (100-62, Won World Series, 4-2, over the L.A. Dodgers.)
15. 1978 New York Yankees (100-63, Won World Series, 4-2 over L.A. Dodgers.)
16. 1980 New York Yankees (103-59, Lost American League Championship to Royals, 3-0)
17. 1985 New York Yankees (97-64, 2nd place A.L. East, 2 GB Toronto)
1994 New York Yankees (70-43, shortened season, finished first.)
18. 1998 New York Yankees (114-48, won WS, 4-0 over Padres.)
19. 1999 New York Yankees (98-64, won WS, 4-0 over Braves.)
20. 2002 New York Yankees (103-58, lost in LDS to Angels, 3-1.)
21. 2003 New York Yankees (101-61, lost World Series 4-2 to Marlins.)
2004 New York Yankees (101-61, lost American League Championship to Red Sox, 4-3)
22. 2006 New York Yankees (97-65, lost in LDS to Tigers, 3-1.)
23. 2009 New York Yankees (103-59, won World Series 4-2 over Philadelphia Phillies.)
24. 2011 New York Yankees (97-65, lost in LDS to Tigers, 3-2.)
O. Franchise currently known as TORONTO BLUE JAYS (1):
1985 Toronto Blue Jays (99-62, Lost AL Championship to KC Royals, 4-3.)
P. Franchise famously known as MONTREAL EXPOS and currently known as the WASHINGTON NATIONALS (2):
1. 1994 Montreal Expos (74-40, 1st place in NL and NL East (6 Games Ahead of Atlanta Braves when strike-shortened season ended)
2. 2012 Washington Nationals (98-64, lost in LDS to Cardinals, 3-2.)
(2017)
Q. Franchise currently known as St. Louis CARDINALS (14):
1. 1942 St. Louis Cardinals (106-48, Won WORLD SERIES, 4-1 over the Yankees.)
2. 1943 St. Louis Cardinals (105-49, LOST the World Series 4-1, to the New York Yankees.)
3. 1944 St. Louis Cardinals (105-49, won W.S., 4-2, over St. Louis Browns*)
4. 1945 St. Louis Cardinals (95-59, finished 2nd, 3 GB Chicago Cubs)
5. 1946 St. Louis Cardinals (98-58, won WS 4-3, vs. Boston Red Sox)
6. 1949 St. Louis Cardinals (96-58, 2nd place, NL, 1 GB Brooklyn Dodgers)
7. 1967 St. Louis Cardinals (101-60, WORLD SERIES WINNERS, vs. Red Sox (4-3))
8. 1968 St. Louis Cardinals (97-65, lost World Series to Detroit Tigers, 4-3)
9. 1985 St. Louis Cardinals (101-61, lost World Series to Kansas City Royals)
10. 2002 St. Louis Cardinals (97-65, Lost National League Championship to SF Giants, 4-1)
11. 2004 St. Louis Cardinals. (105-57, lost WS 4-0 to Boston Red Sox)
12. 2005 St. Louis Cardinals (100-62, lost National League Championship to the Houston Astros)
13. 2013 St. Louis Cardinals (97-65, lost World Series, 4-2, Red Sox.)
14. 2015 St. Louis Cardinals (100-62, lost in LDS to Chicago Cubs.)
R. Franchise currently known as NEW YORK METS (6):
1969 New York Mets (100-62, WORLD SERIES WINNERS, 4-1 over Baltimore Orioles.)
1985 New York Mets (98-64, 2nd place, 3 GB St. Louis Cardinals in N.L. East)
1986 New York Mets (108-54, WORLD SERIES WINNERS, 4-3 over Boston Red Sox.)
1988 New York Mets (100-60, Lost National League Championship to Los Angeles Dodgers, 4-3.)
1999 New York Mets (97-66, lost NLCS to Atlanta Braves, 4-2)
2006 New York Mets (97-65, lost National League Championship to Cardinals, 4-3.)
S. Franchise currently known as CLEVELAND INDIANS (10):
1. 1948 Cleveland Indians (97-58, won W.S. 4-2 over Boston Braves)
2. 1950 Cleveland Indians (92-62, but finished 4th in AL, 6 games behind the Damn Yankees.)
3. 1951 Cleveland Indians (93-61, 2nd place, 5 GB the Yankees.)
4. 1952 Cleveland Indians (93-61, 2nd place, 2 GB the Yankees.)
5. 1953 Cleveland Indians (92-62, 2nd place, 8.5 GB the Yankees.)
6. 1954 Cleveland Indians (111-43, lost WS, NYG, 0-4.)
7. 1955 Cleveland Indians (93-61, finished in 2nd place, 3 GB the Bum Yankees.)
8. 1995 Cleveland Indians (100-44, lost W.S., 4-2, to Braves)
9. 1996 Cleveland Indians (99-62, lost in LDS, 3-1, to Baltimore Orioles)
10. 1999 Cleveland Indians (97-65, lost in LDS, 3-2, to Boston Red Sox)
(2017)
T. Franchise currently known as the CINCINNATI REDS (10):
1. 1961 Cincinnati Reds (93-61), lost W.S. to NY Yanks, 4-1. (N.L. Champs)
2. 1962 Cincinnati Reds (98-64), finished 3rd in NL, 3.5 GB the San Francisco Giants.
3. 1970 Cincinnati Reds (102-60), lost. The World Series to the Baltimore Orioles, 4-1.
4. 1972 Cincinnati Reds (95-59, lost the W.S. to the A’s, 4-3.)
5. 1973 Cincinnati Reds (99-63, lost N.L.C.S. 3-2 (N.Y. Mets)
6. 1974 Cincinnati Reds (98-64, finished in 2nd place, 4 GB the Los Angeles Dodgers.)
7. 1975 Cincinnati Reds. (108-54, Won W.S., vs. Red Sox, 4-3.)
8. 1976 Cincinnati Reds. (102-60, Won W.S., vs. N.Y. Yankees, 4-0.)
9. 1981 Cincinnati Reds @ 66-42 thru 108 games, 1st in NL West, shortened season.
10. 2012 Cincinnati Reds (97-65, lost in LDS to S.F. Giants, 3-2.)
U. Franchise currently known as CHICAGO WHITE SOX (5):
1954 Chicago White Sox (94-60), outgunned by both the Yankees & the Indians, finished 17 GB in the American League.
1959 Chicago White Sox (94-60), lost the WORLD SERIES to the Los Angeles Dodgers, 4-2. (A.L. Champions)
1964 Chicago White Sox (98-64), finished 1 GB the New York Yankees in 10-team American League.
1983 Chicago White Sox (99-63), lost ALCS to the Baltimore Orioles.
2005 Chicago White Sox (99-63), WORLD SERIES WINNERS, 4-0 over the Houston Astros.
V. Franchise knowns as the CHICAGO CUBS (5):
1945 Chicago Cubs (98-56, lost WS to Detroit Tigers, 4-3.)
1984 Chicago Cubs (96-65, lost NLCS to the San Diego Padres, 3-2.)
2008 Chicago Cubs (97-64, lost LDS 3-0 to Dodgers.)
2015 Chicago Cubs (97-65, lost NLCS to New York Mets, 4-0.)
——
2016 Chicago Cubs (103-58, won WS 4-3, over the Cleveland Indians.)
W. Franchise currently known as BOSTON RED SOX (10):
1. 1942 Boston Red Sox (93-59), 9 GB the New York Yankees
2. 1946 Boston Red Sox (104-50), lost World Series to the St. Louis Cardinals
3. 1948 Boston Red Sox (96-59), finished 2nd in AL, 1 game behind Cleveland.
4. 1949 Boston Red Sox (96-58), finished 2nd in AL, 1 game behind Yankees.
5. 1950 Boston Red Sox (94-60), finished 3rd in AL, 4 games behind the New York Yankees.
6. 1977 Boston Red Sox (97-64), finished 2.5 GB the New York Yankees.
7. 1978 Boston Red Sox (99-64), finished in 2nd place in A.L. East, 1 GB the New York Yankees.
8. 1995 Boston Red Sox (86-58), lost LDS to Cleveland Indians, 3-0.
—-
9. 2004 Boston Red Sox (98-64, WORLD SERIES WINNERS, 4-0 over the St. Louis Cardinals.
10. 2013 Boston Red Sox (97-65, WORLD SERIES WINNERS, 4-2 over the St. Louis Cardinals.
X. Franchise currently known as ARIZONA DIAMONDBACKS (2):
1. 1999 Arizona Diamondbacks (100-62, lost LDS to New York Mets, 3-1)
2. 2002 Arizona Diamondbacks (98-64, lost LDS to St. Louis Cardinals, 3-0)
Y. Franchise currently known as ATLANTA BRAVES (14):
1. 1948 Boston Braves (91-62, lost World Series to Cleveland Indians, 4-2)
2. 1953 Milwaukee Braves (92-62, finished 2nd, 13 GB Brooklyn Dodgers)
3. 1956 Milwaukee Braves (92-62, finished 2nd, 1 GB Brooklyn Dodgers)
4. 1957 Milwaukee Braves (95-59, WORLD SERIES WINNERS, 4-3 over New York Yankees)
5. 1958 Milwaukee Braves (92-62, lost WORLD SERIES to New York Yankees, 4-3) (N.L. Champs)
6. 1992 Atlanta Braves (98-64, lost WORLD SERIES to Toronto Blue Jays, 4-2) (N.L. Champs)
7. 1993 Atlanta Braves (104-58, lost NL Championship Series to Philadelphia Phillies, 4-2)
8. 1994 Atlanta Braves (68-46, occupied 2nd place in N.L. East in shortened season)
9. 1995 Atlanta Braves (90-54, WORLD SERIES WINNER vs. Cleveland Indians, 4-2)
10. 1997 Atlanta Braves (101-61, lost NL Championship Series to Florida Marlins, 4-2.)
11. 1998 Atlanta Braves (106-56, lost NL Championship Series to San Diego Padres, 4-2.)
12. 1999 Atlanta Braves (103-59, lost World Series to New York Yankees, 4-0.) (N.L. Champs)
13. 2002 Atlanta Braves (101-59, lost LDS to San Francisco Giants, 3-2.)
14. 2003 Atlanta Braves (101-61, lost LDS to Chicago Cubs, 3-2.)
Z. Franchise currently known as BALTIMORE ORIOLES (11):
1. 1964 Baltimore Orioles (97-65, finished 3rd, 2 GB New York Yankees in AL)
2. 1966 Baltimore Orioles (97-63, WORLD SERIES WINNERS, 4-0 over the Los Angeles Dodgers)
3. 1969 Baltimore Orioles (109-53, lost WORLD SERIES to New York Mets, 4-1)
4. 1970 Baltimore Orioles (108-54, WORLD SERIES WINNERS, vs. Cincinnati Reds, 4-1.)
5. 1971 Baltimore Orioles (101-57, lost WORLD SERIES, 4-3, to Pittsburgh Pirates.)
6. 1973 Baltimore Orioles (97-65, lost American League Championship to Oakland Athletics, 3-2)
7. 1977 Baltimore Orioles (97-64, finished in 2nd place, AL East, 2.5 GB New York Yankees)
8. 1979 Baltimore Orioles (102-57, lost WORLD SERIES, 4-3 to Pittsburgh Pirates)
9. 1980 Baltimore Orioles (100-62, finished 2nd place A.L. East, 3 GB New York Yankees)
10. 1983 Baltimore Orioles (98-64, won World Series, 4-1 over the Philadelphia Phillies)
11. 1997 Baltimore Orioles (98-64, lost ALCS to Cleveland Indians, 4-2).