Here is the History that I have. Not sure it is 100% accurate for Real Life Baseball but I do believe it is what the WIS database has.
16 Original Franchises
NL
Atlanta Braves - Boston Beaneaters:1901-1906,Boston Doves:1907-1910,Boston Braves:1911-1935,Boston Bees:1936-1940,Boston Braves:1941-1952,Milwaukee Braves:1953-1965,Atlanta Braves:1966-2012
Chicago Cubs - Chicago Orphans:1901-1902,Chicago Cubs:1903-2012
Cincinnati Reds - Cincinnati Reds:1901-2012
Los Angeles Dodgers - Brooklyn Superbas: 1901-1910,Brooklyn Dodgers:1911-1912,Brooklyn Superbas:1913,Brooklyn Robins:1914-1930,Brooklyn Dodgers:1931-1957,Los Angeles Dodgers:1958-2012
Philadelphia Phillies - Philadelphia Phillies:1901-1943,Philadelphia Blue Jays:1944,Philadelphia Phillies:1945-2012
Pittsburgh Pirates - Pittsburgh Pirates:1901-2012
San Francisco Giants - New York Giants:1901-1957,San Francisco Giants:1958-2012
St. Louis Cardinals - St. Louis Cardinals:1901-2012
AL
Baltimore Orioles - Milwaukee Brewers:1901,St Louis Browns:1902-1953,Baltimore Orioles:1954-2012
Boston Red Sox - Boston Americans:1901-1907,Boston Red Sox:1908-2012
Chicago White Sox - Chicago White Sox:1901-2012
Cleveland Indians - Cleveland Blues:1901-1902,Cleveland Naps:1903-1915,Cleveland Indians;1916-2012,
Detroit Tigers - Detroit Tigers;1901-2012
Minnesota Twins - Washington Senators:1901-1960,Minnesota Twins:1961-2012
New York Yankees - Baltimore Orioles:1901-1902,New York Highlanders:1903-1912,New York Yankees:1913-2012,
Oakland Athletics - Philadelphia Athletics:1901-1954,Kansas City Athletics:1955-1967,Oakland Athletics:1968-2012
14 Expansion Teams
Los Angeles Angels of Anaheim - Los Angeles Angels:1961-1964,California Angels:1965-1996,Anaheim Angels:1997-2012
Arizona Diamondbacks - Arizona Diamondbacks:1998-2012
Colorado Rockies - Colorado Rockies:1993-2012
Houston Astros - Houston Colt 45's:1962-1964,Houston Astros:1965-2012
Miami Marlins - Florida Marlins:1993-2011,Miami Marlins:2012
Kansas City Royals - Kansas City Royals:1969-2012
Milwaukee Brewers - Seattle Pilots:1969,Milwaukee Brewers:1970-2012
New York Mets - New York Mets:1962-2012
San Diego Padres - San Diego Padres:1969-2012
Seattle Mariners - Seattle Mariners:1977-2012
Tampa Bay Rays - Tampa Bay Devil Rays:1998-2007,Tampa Bay Rays:2008-2012
Texas Rangers - Washington Senators:1961-1971,Texas Rangers:1972-2012
Toronto Blue Jays - Toronto Blue Jays:1977-2012
Washington Nationals - Montreal Expos:1969-2004,Washington Nationals:2005-2012
Defunct Federal League Teams
Buffalo Feds:1914-1915
Indianapolis Hoosier Feds:1914
Newark Peppers:1915
Kansas City Packers:1914-1915
Pittsburgh Rebels:1914-1915
Baltimore Terrapins:1914-1915
St. Louis Terriers:1914-1915
Brooklyn Feds:1914-1915
Chicago Whales:1914-1915